Vice President Bush tried to round up stray votes for the administration tax bill in three southern states today, charging that the Democratic alternative offers only an illusory "Catch 22" promise of strengthening the economy and lowering inflation and interest rates.

On a 12-hour jet hop that touched down in Atlanta and Baton Rouge en route here, Bush sought to build public pressure to force wavering Democratic congressmen to back Reagan's three-year, 25-percent cut in the showdown House vote Wednesday. His trip cost the Republican National Committee an estimated $25,000.

He said in Baton Rouge that the administration bill embodies "true tax reform." But, with the Republican govenors of Louisiana and Texas nodding agreement, he also pointed out that it offers a better deal for the oil producers of these energy-rich states.

The Bush tour was ordered Friday as part of a last-minute administration drive to corral votes of "boll weevil" conservative southern Democrats, whose support gave Reagan his narrow House victories earlier on budget and spending bills.

On those votes, anywhere from 12 to 21 Democrats from the three states Bush visited jumped party lines to vote with the president. As many as eight reportedly were wooed back in line by oil industry concessions included in the tax bill sponsored by Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.). Bush, an oil industry product himself, bore down heavily on those aspects of the rival bills.

He told the Baton Rouge press club the administration bill would do twice as much for "very many, very small oil royalty owners," and put more money in the pockets of operators of stripper wells and those who discover new oil.

Bush said the two-year Democratic bill offered only the "illusory" promise of a third year of cuts, because the economic triggers specified for the third year, copied fromthe administration's forecasts, could not be reached unless the Reagan bill is passed. Calling it a "Catch 22" proposition, he said, "They use our criteria, but they don't give us the tools to get there."

In seeking to build public pressure on wavering Democrats, Bush told audiences that "we're up against some political pros [Rostenkowski and House Speaker Thomas P. (Tip) O'Neill Jr.] who are interested in only one thing -- to win, to win."

He conceded that as a result of the oil industry and other business concessions, the Democratic bill had become "less objectionable." Bush also conceded there were vote seeking "compromises" by the administration last week but insisted "the president is standing on the fundamentals" of his position.

Bush addressed small audiences in the improved tour, but aides said they hoped television and press coverage in the three states would aid to local efforts by business groups to persuade wavering Democrats to back the president's bill.