William A. Borders Jr., a prominent Washington lawyer and member of the D.C. commission that selects the city's judges, was arrested yesterday afternoon at an Arlington motel and charged in connection with an attempt to bribe a federal judge in Miami.

The FBI alleged in a sworn statement that Borders, past president of a national association of black lawyers, accepted a total of $150,000 in cash in an effort to secure reduced sentences for two brothers who had been convicted and sentenced by District Judge Alcee L. Hastings. The judge, who was reportedly in Washington for a testimonial last night honoring Borders, was not charged.

Law enforcement sources said Borders had met Hastings earlier in the day at National Airport and the two later went to the lawyer's Washington office. The FBI was seeking the judge last night for questioning and Justice Department sources said that they intend to present evidence concerning the case to a federal grand jury in Miami.

In the sworn statement, filed in federal court in Alexandria, the FBI said that Borders met three times between Sept. 12 and yesterday with an undercover agent posing as one of the brothers and had accepted $25,000 as the first installment of the $150,000. His arrest yesterday came after he allegedly accepted the remaining $125,000 in the motel's parking lot.

The FBI affidavit said the investigation of Borders began after Borders told a confidential U.S. informant that Judge Hastings was soliciting bribes from criminal defendants who appeared before him.

The FBI statement said that on Tuesday, three weeks after Borders received the $25,000 in "up front money," Judge Hastings issued an order overturning part of a prior ruling in which he had ordered the two brothers to forfeit $1.2 million in property. The property has been taken by the government as part of the penalty given the brothers following their conviction on federal racketeering charges.

Borders was arrested yesterday at the Twin Bridges Marriott where he allegedly had gone to meet the undercover agent for completion of the alleged payoff. He appeared later at a 30-minute hearing before a U.S. magistrate in Alexandria where his bond was set at $25,000.

Borders, 42, looking grim and subdued, said little, answering "Yes, sir," when asked by Magistrate W. Harris Grimsley if he understood the charge and the possible penalty if convicted.

The alleged offense, interstate travel to promote or facilitate bribery, carries a maximum penalty of five years in jail or a $10,000 fine or both.

Reid Weingarten of the Justice Department's public integrity section, together with Gerald McDowell, the section chief, and U.S. Attorney Justin Williams, asked Grimsley to set bond at $25,000.

Defense lawyer John Shorter argued against the request, picturing Borders, who until recently headed the National Bar Assoiation, as "very respected" and "a man of integrity." Magistrate Grimsley set bond, saying, "If he's convicted, his career probably will come to an end. Given the temptation, he might flee."

Borders' arrest came just hours before he was to be honored by members of the Washington legal community at a black tie "Gala Celebration Dinner Cruise" on the Potomac.

About 50 people gathered at the foot of Prince Street in Alexandria for the cruise last night, most of them unaware that the guest of honor was in the District of Columbia jail. Shorter appeared briefly at the pier and said that he doubted Borders would be able to attend.

Those who were told of the arrest were stunned. "You're kidding, Borders? When did that happen?" said one of the guests.

Hastings, 45, was appointed to the U.S District Court in 1979 by former President Jimmy Carter, and is the first black to be appointed to the federal court in Florida. He spent two years as a state juvenile court judge in the Fort Lauderdale area and was a longtime civil rights activist. Before he became a judge, he ran unsuccessfully eight times for various political offices, including the U.S. Senate in 1970.

It could not be determined yesterday how long Hastings and Borders have known each other. Law enforcement sources noted that both men attended the Howard University Law School and that Hastings, like Borders, was a member of the National Bar Association.

Judge Hastings gained some notoriety in Florida last year when a Bolivian indicted on cocaine charges skipped out on $1 million bond in his court. Federal prosecutors were upset because Hastings refused to hold a hearing on the source of the bond money.

Attorney General William French Smith has complained in recent speeches that accused drug smugglers have been able to flee prosecution because judges lowered their bond or failed to investigate sources of bond money. Smith said $1 million is "petty cash" to big time drug smugglers.

Last summer Borders became embroiled with the Reagan administration in a dispute over whether he should be allowed to serve out his term on the D. C. Judicial Nomination Commission, to which he was appointed last year by President Carter. The Reagan White House tried to remove Borders from the commission, which nominates candidates for seats on the D. C. Superior Court and the D. C. Court of Appeals, in favor of a lawyer of its own choosing.

Borders filed suit and a District Court judge ruled that Reagan did not have the authority to replace him. The White House has appealed that decision.

According to the FBI's statement, Borders said that for $150,000, the brothers Frank and Thomas Romano, who had been convicted after a trial before Hastings, could get their three-year prison sentences reduced to probation.

Borders then allegedly traveled on Sept. 11 and 12 from Washington to Miami International Airport, where he met an FBI undercover agent. According to the statement, Borders said that in exchange for the bribe, Hastings would show leniency, first by returning some of the brothers' seized property and then by eliminating their jail sentences.

On Sept. 18 and 19, the statement alleged, Borders again traveled to Miami and met the agent who was posing as Frank Romano. At that meeting, the FBI charged, the $25,000 cash changed hands.

In a telephone conversation on Monday from Washington to Miami, Borders allegedly predicted to the agent that Hastings' order returning some of the forfeited property would be forthcoming, according to the statement. The judge's order was issued the next day, according to the statement.

On Wednesday, the FBI asserted, Borders asked the undercover agent to travel to Washington to pay the rest of the bribe. The statement said Borders agreed yesterday to meet the agent at the Marriott, where he was later arrested.