After six years of refusing to legalize betting on horses in Virginia and several days of wrestling with the issue, the House of Delegates yesterday passed and sent to the Senate a bill that would permit construction of race tracks if voters approve.

The 52-to-48 vote came one day after the measure failed by one vote to gain a constitutional majority of 51 votes because one supporter had left town for a once-a-year business meeting. Horse race betting advocates gained two votes yesterday when that man, Del. J. Waren White (D-Norfolk) flew back from his meeting early, and when minority leader Jerry Geisler (R-Hillsville) switched his vote.

Geisler said he changed his vote because the issue was so "significant" that the voters should decide whether or not to legalize race tracks in a referendum next November. If the Senate passes the bill as expected, that referendum would be on the ballot next fall.

Geisler said he has no strong feelings about the morality of horse racing and would have voted for it Wednesday if he had known White's absence would cause the bill to fail. He said he had not discussed the issue with Republican Gov. John N. Dalton, who said during his campaign last fall he would support the establishment of parimutuel betting.

Although the measure failed on Wednesday, it came back for another vote because the House voted to reconsider it, and then the bill's chief sponsor, Del. Raymond R. Guest Jr. (R-Front Royal) moved to putt off reconsideration until yesterday in the hope that White would return.

In the interim both horse-racing industry representives and other delegates offered to send a private plane to fetch White, but he took a commercial flight.

If racing is approved in the referendum, a five-member racing commission would be appointed by the governor. Localities would have to have separate referendums before race tracks could be established in their particular areas.

Del. Richard R.G. Hobson (D-Alexandria), floor leader of the opposition, said yesterday he expected the bill to pass the Senate but that opponents of legalized gambling would be organizing immediately to defeat it in the referendum.

The name of Del. Warren E. Barry (R-Fairfax) name was inadvertenly left off the list of Northern Virginians voting against the bill yesterday.