Vice President Bush holds an enormous lead over his nearest likely adversary for the Republican 1988 presidential nomination and Sen. Gary Hart (Colo.) is substantially ahead of other Democrats, according to a new Washington Post-ABC News public opinion poll.

This early measure, taken in polling from May 15 to May 19, also shows Bush and Hart running neck-and-neck in a presidential trial heat, with the Democrat ahead by 47 percent to 46 percent among all people interviewed and by 49 percent to 45 percent among registered voters. Bush holds large leads over other possible Democratic opponents.

Asked to select their favorite GOP nominee from a list of seven names, 58 percent of the potential Republican primary voters interviewed chose Bush. Far behind but leading the rest of the pack with 14 percent was Howard H. Baker Jr. of Tennessee, the former Senate majority leader. Third, at 12 percent, was Sen. Robert J. Dole (R-Kan.), the majority leader.

Rep. Jack Kemp (R-N.Y.) placed sixth, supported by 4 percent. Ahead of him were television evangelist Marion G. (Pat) Robertson at 6 percent, and former U.N. ambassador Jeane J. Kirkpatrick with 5 percent. Sen. Paul Laxalt (R-Nev.) was last with 2 percent.

Figures for the Republicans include responses from 436 people who said they are Republicans and 265 who said they are independents who lean Republican, many of whom may vote in a Republican primary.

On the Democratic side, 33 percent of the Democrats and independents leaning Democratic selected Hart from a list of nine potential candidates. Second, at 19 percent, was Chrysler Corp. Chairman Lee Iacocca, who has said he will not be a candidate. Third was the Rev. Jesse L. Jackson, at 18 percent, slightly ahead of New York Gov. Mario M. Cuomo, at 16 percent.

Other Democrats mentioned and their scores are Sen. Bill Bradley (N.J.), 6 percent; former Virginia governor Charles S. Robb, 5 percent; Rep. Richard A. Gephardt (Mo.), 2 percent; Sen. Joseph R. Biden (Del.), 1 percent, and Arizona Gov. Bruce Babbitt, less than 0.5 percent.

Hart might have scored substantially higher had Iacocca not been included on the list. Both had sharply more appeal than the others among independents leaning Democratic, many of whom may vote in Democratic primaries, suggesting that Iacocca siphoned off support that would otherwise have gone to Hart.

Jackson was supported by 55 percent of the blacks likely to vote in a Democratic primary and by 7 percent of the whites.

Cuomo did better than any other candidate in the East, getting 34 percent in that region, compared to 26 percent for Hart. In the South, Hart placed first with 31 percent, followed by Jackson with 27 percent. Hart led by wider margins in the Midwest and West.

These Democratic results are based on the views of 496 people who said they are Democrats and 198 independents who lean Democratic.

In the presidential trial heat between Bush and Hart, several factors emerged that could be meaningful in 1988, despite the remoteness of that campaign. The two run basically even among independents, with a slight edge for Hart. Independents voted strongly Republican in the past two elections when Ronald Reagan led the ticket.

In addition, Hart leads in every age group except for people 18 to 30, where Bush performs strongly. But younger Americans have proven the least likely to vote, suggesting that Hart's real lead could be higher.

Finally, Bush shows little sign of benefiting from Democrats voting Republican, a major factor in Reagan's two wins. The poll shows Bush picking up 5 points or so in crossover voting, while Reagan gained more than 20 points.

In other trial heats in the survey:

*Bush led Iacocca by 52 percent to 40 percent among all 1,506 people interviewed and 50 percent to 42 percent among the 1,139 registered voters surveyed.

*Bush led Cuomo by 62 percent to 29 percent overall and 61 percent to 31 percent among registered voters. And Bush led Jackson by 66 percent to 26 percent among all surveyed, and 68 percent to 25 percent among registered voters.

Theoretically, in 19 cases out of 20, a poll this size is subject to a sampling margin of error of about 3 percentage points.