The Senate, after only 20 minutes of debate, voted 93 to 0 yesterday to confirm President Reagan's nominee, William J. Bennett, as secretary of education.

Bennett, 41, succeeds T.H. Bell, who resigned a month ago to return to Utah and teach. Although the vote for Bennett was unanimous, several Democrats said they were concerned that Bennett might not oppose forcefully enough the education program cuts that Reagan included in his 1986 budget request.

The Senate also confirmed Donald P. Hodel as secretary of the interior and John S. Herrington to replace Hodel as energy secretary. The vote for each was 93 to 1, with Sen. William Proxmire (D-Wis.) voting against the nominees.

The membership of a steering committee put together by House Majority Leader James C. Wright Jr. (D-Tex.) to help him become speaker in 1986 may indicate that he faces less opposition than many Democrats had assumed.

Among those who have agreed to back Wright, according to the majority leader, are Reps. Richard A. Gephardt (D-Mo.), who many younger lawmakers had hoped would be their standard-bearer for speaker, Tony Coelho (D-Calif.), head of the Democratic Congressional Campaign Committee, and John P. Murtha (D-Pa.), a close political ally of another possible contender, House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.)

Wright, who will hold a news conference today to discuss his candidacy for speaker, says he has already received commitments for support from more than two-thirds of the House's 251 Democrats, which should assure him of becoming speaker provided the Democrats still control the House after the 1986 elections. "I'm very gratified," Wright said.

According to several Democrats, Gephardt told Wright earlier this week that he would not run for speaker in 1986, when incumbent Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) has said he will retire, but would back Wright instead.

"I think Jim Wright ought to be the next speaker," Gephardt said yesterday. "He has done a good job as majority leader."

Coelho, according to Democrats, is interested in running for majority whip, third in command after speaker and majority leader. However, two other Democrats also are interested in that post: Reps. William V. (Bill) Alexander Jr. (D-Ark.), currently chief deputy whip, and Charles B. Rangel (D-N.Y.).

The Republicans finally finished sorting through several dozen requests and selected four new Republican members of the House Permanent Select Committee on Intelligence. They are Reps. Henry J. Hyde (Ill.), Dick Cheney (Wyo.), Robert L. Livingston (La.) and Bob McEwen (Ohio).

Last week Speaker O'Neill appointed seven Democrats to vacancies on the committee. They are Reps. Robert A. Roe (N.J.), George E. Brown Jr. (Calif.), Matthew F. McHugh (N.Y.), Bernard J. Dwyer (N.J.), Dan Daniel (Va.), Robert W. Kastenmeier (Wis.) and Anthony C. Beilenson (Calif.).