Vice President Bush yesterday performed for the first time his only constitutional duty -- presiding over the Senate -- and made a short speech sayng that as a former House member and son of a former senator he was glad to be back. Since he is not a senator, Bush needed special permission to say anything beyond issuing parliamentary rulings.

He was warmly welcomed by both party leaders. Majority Leader Howard H. Baker Jr. (R-Tenn.) noted that Bush holds a unique position as a member of the executive branch who is also president of one part of the legislative branch. He added, "You belong to us and we're glad you're here." lMinority leader Robert C. Byrd (D-W.Va.), a master of the complex Senate rules, said he would be glad to advise Bush on rulings.

Bush spent much of yesterday afternoon presiding over the confirmation of President Reagan's Cabinet members. But if he follows the practice of his predecessors that will be about the last the Senate sees of him except when he is needed to break a tie or make an important parliamentary ruling. The rest of the time he will be out performing whatever chores the president thinks up for him.