President Reagan bid for Democratic support for his tax-overhaul plan today, praising tax-reform advocate Sen. Bill Bradley (D-N.J.) and soft-pedaling the partisanship that has been a feature of some of the president's speeches.

"Your senior senator is a pioneer of the tax-reform movement," Reagan told a crowd of several thousand persons. "We admire Bill Bradley, we're glad he's on the team, and his leadership is indispensable to victory."

Reagan's words drew applause from the crowd but a restrained response from Bradley, who was not present.

The senator said through a spokesman that he is "delighted" that Reagan was campaigning in New Jersey for the tax package but had reservations about the generous deductions allowed for capital gains and oil and gas drilling costs in the president's proposal.

Bradley also differs with Reagan on state and local income-tax deductions, which would be disallowed on federal tax returns under the president's plan but are partially permitted in a rival measure by Bradley and Rep. Richard A. Gephardt (D-Mo.).

Reagan today defended the elimination of this deduction and said "it's simply not true" that it would "hurt the people who pay those taxes in the high-tax states."

The remark appeared to be directed at New York Democratic Gov. Mario M. Cuomo, a leader in the effort to keep this deduction, although Reagan did not mention him by name.

White House spokesman Larry Speakes said, "We're not trying to single out New York."

Reagan also did not mention the word "Republican" in his speech and generally followed the bipartisan approach advocated by House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill)., whom the administration is counting on to push the tax package.

Rostenkowski complained recently that Reagan was limiting the bipartisan appeal of his tax plan by undertaking road trips in which he combined tax speeches with Republican fund-raisers where he sharply attacked the Democrats.

Today, Reagan referred only to unnamed adversaries. He denounced the "powerful and privileged" who "use tax shelters to keep from paying their taxes" and said, "The sharks are circling our tax plan, ready to take a bite."

"We happen to have a foolproof shark repellent in the will of the American people . . . , " Reagan added.

Last week, in Oklahoma City, Reagan defended the elimination of state and local tax deductions by saying, "I just don't believe the good people of Oklahoma or other low-tax states" should pay for the "lack of resolve" of governments in high-tax states.

In New Jersey, the president shifted the focus of his argument, saying that current law is unfair to the two-thirds of taxpayers who do not itemize and therefore are not benefited by state and local deductions. Reagan also said that "I don't consider New Jersey to be a high-tax state," even though various studies rank it among the top 10 states in per capita taxes.

In denouncing the federal tax system as "inherently unjust," Reagan borrowed a Marxist phrase used to describe the supposed fate of capitalism, saying, "We all know our current tax system is ready for the ash heap of history."

The president also claimed that his tax plan would "ensure the growth of the American economy in our time and in our children's time."

"And we're not just predicting economic growth -- we're promising it," Reagan said.

The president was frequently applauded by the friendly crowd, but there were a sprinkling of signs opposing aid to the Nicaraguan rebels.

Reagan is scheduled to make a Flag Day speech today in Baltimore and campaign for the tax plan next week in Indianapolis and Dallas.