George Bush scored steadily against the Democratic opposition, while Geraldine A. Ferraro started out shaky and finished strong in the televised debate here tonight between the vice-presidential rivals.

Both camps expressed satisfaction with their contenders' performance, but neither thought the debate by itself would have a major impact on the race.

Democrats had hoped that a powerful performance by Ferraro would produce further gains, after Walter F. Mondale's besting of President Reagan in the Louisville debate last Sunday night, but Bush -- in the estimates of both parties -- more than held his own.

Ferraro, the three-term Democratic House member from Queens, N.Y., was the focus of public interest as the first woman on a national ticket, and she did nothing to embarrass herself or her party.

She stood toe-to-toe with the incumbent vice president in an emotional exchange on terrorism, telling him, "I almost resent . . . your patronizing attitude that you have to teach me about foreign policy."

With her characteristic fast-paced New York talk slowed to a comfortable gait, she delivered a closing statement defining patriotism in Democratic terms that attained a level of eloquence.

But Ferraro often had her head buried in her notes, both at the start of the debate and in the foreign policy section, and was guilty of obvious filibustering when asked how she and Mondale thought a nuclear freeze could be verified.

It seemed questionable to most observers whether Ferraro had done much to convince the doubters that she was qualified to be a heartbeat from the presidency. Former Carter administration aide Stuart Eizenstat said Ferraro "crossed the threshold of credibility," but Reagan campaign pollster Richard B. Wirthlin said he saw "nothing that will move the six out of 10 people [in surveys] who think she was chosen only because she was a women."

Bush spoke directly to the television audience from beginning to end of the debate, seeming to need no prompting from his notes. For the most part, he brushed Ferraro aside, while taking the case directly -- and aggressively -- to Mondale.

But as he often does on the stump, Bush compromised his independent stature by turning himself into a Reagan cheerleader, performing verbal handsprings in his effort to whip up enthusiasm for the leader of the free world."

But his assurance grew as his decibel level diminished during the course of the debate, and the impression of viewers here was that people who knew nothing of the resumes of the two debaters would have had no difficulty judging Bush the more experienced.

At the minimum, he appeared to have avoided the kind of upstaging by Ferraro that Reagan suffered at Mondale's hands in Louisville. Such an event would not only have compounded Republican problems in holding the lead in the election but clouded Bush's chances of gaining the presidential nomination in 1988.

Still, he must have come away with greater respect for Ferraro as an opponent, because the one time he attempted to challenge her directly, she slapped him down.

It came in a discussion on terrorism and the CIA. Bush criticized her for seeming to "do away with all covert activity" by the CIA and offered to "help you [Ferraro]" understand the difference between the Iranian and Lebanese situations. He also said the Democrats had better not tell the families of the Marines who died in Lebanon that they had "died in shame."

Ferraro rebuked him sharply for his "patronizing attitude" and, with genuine anger, told him, "Please do not categorize my answers." She denied strongly that there was any implication of "shame" for the casualties, and generally left Bush eager for the topic to change -- which it did before he had to reply.

If that was Ferraro's best moment, there were many awkward ones for her. She seemed halting in her explanation of the Mondale approach to arms control, and less than confident in the economic statistics that appeared to be inscribed in her notebook.

Predictably, the final 45 minutes on foreign policy played to Bush's strength, as the former ambassador and CIA director displayed his knowledge of Central American, Mideast and arms-control issues. Ferraro fared well in laying out broad Democraatic disagreements but sagged visibly on several occasions when she attempted to spell out the details of that policy.

The subject matter of the debate's domestic section kept her more on the defensive than her running mate had been in Louisville. She and Bush had to discuss theri income tax and financial disclosure policies and their views on religion. But Bush was more aggressive on the first topic that she was and managed to shift the subject of religion into a chance to remind viewers that Reagan had appointed the first woman Supreme Court justice.

Though he came here burdened by a reputation as verbally slowfooted, Bush found the words that eluded Reagan on Sunday and delivered a thematic closing and statement contrasting the "hope and opportunity" of Reagan's leadership with the "weakness and failed policies" of the Democratic past.

Ferraro found her way to basic Democratic themes of economic fairness and disarmament in her well-rehearsed closing statement, but she missed some other targets her aides had laid out. The subject of Social Security, where Mondale had put Reagan totally on the defensive, did not cross her lips; the deficit issue was also brushed aside.

But both managed to do basically what they had set out to do. Ferraro managed to hold the stage with Bush and, to that extent at least, show that she was not out of her league. And Bush managed to be firm and agressive without ever beating up on the lady.

With that result, chances are that the spotlight will shift quickly back to Mondale and Reagan.