Prudential Insurance Co., which three weeks ago surprised the financial community when it announced it wanted to acquire the big brokerage house Bache Group Inc., said today that more than 51 percent of Bache's outstanding stock had been offered to the insurance giant at $32 a share.

With more than half of Bache's stock in Prudential's hands, the merger is assured of being approved at a Bache stockholder meeting that Prudential said will occur in June. Purchasing Bache will cost Prudential about $385 million.

The success of the Prudential offer also quashes any speculation that the Belzberg brothers of Canada, who own 22.6 percent of Bache, the nation's eighth-biggest broker, will make a counteroffer. The Belzbergs -- Samuel, Hyman and William -- have been buying Bache stock steadily since early 1979 and said early this year that they might consider trying to take over Bache.

Nevertheless, Samuel Belzberg asked Bache President Harry A. Jacobs for two seats on Bache's board, a request that Bache directors turned down. Fearing that the Canadians would try to gain a majority interest in the firm, Jacobs turned to his financial advisers, the First Boston Corp., to find a possible merger partner.

Within two weeks, First Boston put together the cash merger between Bache and Prudential.