An Alexandria man was convicted yesterday of running an illegal bingo game in the city and fined $1,000 with $500 suspended. It was the first case to reach trial since an investigation was begun into alleged irregularities in Alexandria bingo operations.

James R. Fike was found guilty of operating a bingo without a license last Jan. 17 in the name of B & J Specialties, a manufacturer of items such as desk sets.Fike's attorney, James M. Lowe, said he would appeal General District Court Judge Martin E. Morris's decision to Alexandria Circuit Court.

At the trial yesterday, Lowe argued that his client had applied last Dec. 25 for renewal of the bingo permit he held in the name of B & J Specialties, and that he had never received a letter from Alexandria Finance Director Howard Holton informing him that the license would not be renewed.

"I assumed that it was tied up in the mail," Fike said of the Holton letter, adding that another group which sponsored bingo games in the same hall had received its new license 12 days late. Fike's attorney argued there was no proof that the letter had ever been mailed.

Under Virginia law, only nonprofit or charitable organizations may sponsor bingo games and these must have been in existence for at least two years. In his letter to Fike, Jan. 6, Holton contended that B & J Specialties failed to meet these requirements.

Holton and Charles Townsend from the Alexandria Finance Department visited the bingo parlor at 4603 Duke Street on Jan. 17 and discovered that Fike was operating a bingo game without the required permit. Both Fike and Holton testified yesterday that Holton did not ask Fike to close down the game that night. On April 7 a warrant was served on Fike and he was arrested.

A second man, John Keator, has been arrested on charges of operating illegal bingo games. Special Bingo Prosecutor Edward J. White said yesterday that Keator's trial is scheduled for next month.

Fike acknowledged under cross-examination that he did not know whether B & J Specialties is listed as a stock company or a nonprofit group. He also said he did not know exactly how many members belong to the youth group that was supposed to receive the receipts from the bingo games. But he rejected White's contention that such a group had never existed and that the 1977 bingo application filed by Fike contained incorrect statements.

Judge Morris, who is from Fairfax, presided because the two Alexandria General District Court Judges, Robert T. S. Colby and Daniel F. O'Flaherty, preferred that a judge from another jurisdiction hear the case.