Bill Bradley used to joke about having the only 88-year-old body in the National Basketball Association. He claimed he really didn't have that much natural ability. Others could run faster and jump higher. His arms were so weak he had trouble doing 20 push-ups. When he went up for a jump shot, his feet barely left the floor.

Poor Bill Bradley. In 10 seasons as a pro, he scored 9,217 points and played on two world-championship teams.

Bill Bradley used to say that everyone at Princeton was smarter than he was, so he had to study twice as hard. When he went to the library, he took an electric fan to drown out distracting noise.

Poor Bill Bradley. He graduated with honors in history and won a Rhodes scholarship.

Bill Bradley is in his third year as the junior senator from New Jersey, and, in his self-deprecating style, he would probably say that he is just plugging along, trying to hold his own in the august company of the U.S.Senate.

So it should come as no surprise that poor Bill Bradley has developed a reputation as one of the hardest working and most thoughtful young Democrats in the Senate, a genuine favorite of his older collegues.

He is treated as a celebrity among celebrities, everyone's favorite son. Perhaps this is understandable; sports, after all, transcend politics. They are competitive, all-American, the only real source of modern-day heroes. Every senator who has spent his life in the humdrum pursuit of money, votes and power can respect that.

Ask Sen. Wendell H. Ford (D-Ky.), a politician's politician, why he invited Bradley to campaign for him, and he says: "He's liked, liked, easy to get along with and hard worker." Then he adds, "He's an attraction. He still holds the record of most points scored in the Kentucky Invitational Tournament."

Bradley has been picked to head a Democratic advistory group charged with responding to President Reagan's economic plan, is vice chairman of the Senate campaign committee and is well-enough committee and is well-enough thought of back home for a New Jersey magazine to ask on its March cover: "Senator Bill: Does this look like a future president of the United States? Did Jimmy Carter? Look closely."

You won't read much about Bill Bradleyu in Washington, though. As a basketball player, he had a theory about this. He wrote about it in his book, Life on the Run:

"Basketball players and politicians have at least one thing in common. They meet the press almost every working day. In basketball, the interaction leads to a charade. Reporters try to leads to a charade. Reports try to lead players to statements which will confirm the reporters' own preconceptions and players try to avoid saying anything that will make them look had. . . . Among the press, players get reputations as being good copy or bad copy, depending on their quips and cooperation. I'm bad copy."

As a senator, Bradley admits, "I haven't been much copy at all."

Part of this is deliberate. He is essentially a private person who has had more than his share of adulation during his 37 years and is leery of it. As a two-time all-American and Olympic basketball star, he became a symbol of the Christian-athlete-scholar as a college student, and had a book-length profile written aobut him in The New Yorker magazine when he was 21.

He is also extremely ambitious and disciplined. For years, people have been suggesting that he eouls be president someday.Now it doesn't sound so far-fetched.

By nature, he is a team player. He has succeeded in athletics and politics by practicing fundamentals, not grandstand plays. He has the somewhat novel belief that a senator should know what he is talking about before he shoots off his mouth, or his duplicating machine.

So he confines his public remarks to the relatively narrow subjects in which he has developed expertise, or matters affecting New Jersey. Even here there is a canny logic. To the layman, the single issue he has spent the most time on, the strategic petroleum reserve, sounds like an esoteric one with no constituency.

But the battle over setting aside large stockpiles of oil for use in emergencies enables Bradley to talk about energy, national defense, economics and international affairs all at once. And if an emergency ever develops and the government's reserves are inadequate, as Bradley maintains, he will be regarded as a futurist.

Bradley is comfortable with questions about his days as an athlete, although he doesn't follow basketball anymore and has attended only three games since he retired from the sport.

He realized that his celebrity status as a basketball player was a plus and a minus for a new senator. As a candidate, he recalls issuing "these highly substantive statements" and the subsequent press reports invariably beginning, "Bill Bradley, former New York Knick, today said. . . . "

It became a joke with him, and when he won the election, a campaign adviser sent him an impressive office nameplate: "Sen. Bill Bradley, former New York Knick."

It would be an understatement to say Bradley isn't the smoothest, fastest-talking or most dynamic new voice in the Senate. His oratory is wooden. He lacks the smoothness and easy grace that come naturally to most politicians.

With his stooped shoulders, rumpled suits and long hurried strides, he often looks like a disheveled college professor perpetually a half-hour late for class, aloof and distracted.

Bradley reached the Senate without one iota of legislative experience. But he gained a reputation as a workaholic, arriving at his office early and leaving late. Today it is hard to find anyone to say anything bad about him.

Ask a natural opponent like New Jersey GOP Chairman David Norcross what he thinks about Bradley, for example, and you get this: "He's a nice man. we get along well. He's my friend. But, all things being equal, I'd rather we had a Republican senator."

The New Jersey Democrat has nurtured an image as a thoughtful legislator.

Thomas Cochran, execuctive director of the Northeast-Midwest Coalition, recalls candidate Bradley telephoning for a briefing. They arranged a breakfast meeting. Cochran is no novice at dealing with politicians, and he arrived expecting the worst.

"The idea of a basketball player in the U.S. Senate kind of frosted me. I was ready to be turned off," he recalls. "I do a lot of this kind of thing, and I came thinking I'd have 15 minutes to make my pitch and would have to complete with an entourage of aides and hangers-on."

Bradley arrived alone. He grilled Cochran for almost two hours, scribbling everything he heard into a small notebook. The session ended only when Cochran had to leave for another meeting. Bradley then arranged for a second session with Cochran's staff. Cochran was impressed.

"Bradley is tenacious," he says. "He's very much the workhorse, not the racehorse."

A second incident occurred shortly after Bradley was sworn into the Senate. A reporter, on his way to another assignment, glanced down at the Senate floor one morning and noticed the 6-foot-5 senator huddled in the back of the chamber with an older man and a black book. When the reporter returned four hours later. Bradley and the elderly man were still there, deep in convensation.

The man turned out to be a retired Senate parliamentarian. He and Bradley were going over Senate rules, line by line. The new senator didn't give his first floor speech for three months, and then it was on essentially a pork-barrel issue, repairing the aircraft carrier Saratoga in the Philadelphia Navy Yard, where hundreds of New Jersey voters are employed.

During his first two years in office, Bradley devoted himself to work on the Finance and Energy committees, getting to know the personalities of the Senate and putting together an impressive staff. Although he appeared non-ideological, his voting record was that of a traditional northern liberal, firmly committed to the Carter administration. He supported President Carter's position 88 percent of the time, and seldom voted against the wishes of organized labor.

It was the defeat of Carter and a host of senior Senate Democrats that gave Bradley his greatest opportunity for success -- or failure. As the stunned Democrats regrouped, Bradley was appointed vice chairman of the party's Senate Campaign Committee and, more importantly, head of an advisory economic group that included in its membership a host of senior senators.

Minority Leader Robert C. Byrd (D-W.Va.) says he picked Bradley to chair the group because "he impressed me as being a worker, as someone who is bright and knowledgeable and enjoys tackling a problem and coming up with a compromise to solve it."

The group was charged with fashioning a response to Reagan's budget and economic plan, no easy task. "Democrats are uncertain," says Bradley. "We're in a period of real turmoil and dramatic shifts. I think there's no firm ground you can walk on and not be sure it won't cave in."

The group met for weeks, and then took their recommendations to the Democratic Caucus, which discussed them in an extraordinary series of meetings that dragged on for three days. Bradley calls these sessions "very important as we try to develop a new consensus, a new agenda for the '80s."

Democrats agreed on a loosely drawn set of priorities to challenge

Reagan budget cuts on the Senate floor. "I didn't expect to win many votes, but I thought it was important we make the record and define what issues were important to us," says Bradley.

The Democrats were killed on the floor. The once-powerful party was divided and in disarray. They didn't make a dent in Reagan's budget.

In defeat, Bradley looked like a frustrated floor, sometimes grabbing a microphone to speak on a favorite amendment, then striding hurriedly to the back of the chamber, then chatting with a colleague.

It was like his old days with the Knicks. "They always said I moved best without the ball," Bradley said later.