Alexandra's finance director has denied a new bingo permit to the private school whose bingo games figured prominently in the recent bribery trial of Alexandria prosecutor William L. Cowhig.

Howard J. Holton, the finance officer, said he denied the 1979 permit to the Montessori School of Alexandria because of past "admitted irregularities." He declined in an interview last night to be more specific.

According to the indictment brough against Cowhig, he failed to prosecute the school's director for running allegedly illegal and highly lucrative bingo game to raise money for the school.

Cowhig was acquitted Dec. 14 of charges that he asked for and received $32,000 in bribes from the school director, Dirgham Salahi.

Salahi testified during the seven-day trial that he made cash payments of $500 a week to Cowhig from jan. 4, 1977 to May 1, 1978 to buy "peace" from "harassment" by the prosecutor, who he said had threatened repeatedly to shut down the Montessori games.

Salahi, who has called the games the lifeblood of the school, could not be reached last night.

Holton said an application for a new yearly permit for the school was filed Thursday. He said he gave notice of rejection in a registered letter sent Friday.

Rejection may be appealed to the city council, Holton said.

A parent familiar with the bingo operation said the decision would be appealed.

"I think a lot of the parents are very upset about it," Charles Craven said of the rejection. "We had nothing to do with the Cowhig trial."

He said the school would have to continue paying rent at the auditorium where the game have been held.

Holton said Alexandria issues permits for bingo under a city ordinance that comforms with state law. Virginia's gambling law was amended in 1974 to permit bingo games under certain conditions.