Myers said the debate would be run by a moderator, and would be held after the April 6 candidate filing deadline, so late filers could participate.
The town election is May 12.
Bowers was fired last August by unanimous decision of the mayor and Town Council. He sued the town on Sept. 29, asking for reinstatement, back pay and benefits. He said he was not given a chance to defend himself prior to his firing.
A judge dismissed Bowers' suit on Dec. 3. An appeal of that decision is pending.
Myers on Thursday took issue with comments made by Bowers when he announced his candidacy last week.
Bowers accused Myers of being power hungry, and with micromanaging the town. He said he would give free rein to department heads if elected.
He also accused Myers and the Town Council of ruining his law enforcement career without just cause. He called for an ethics commission to be formed to protect against improper influences in government affairs.
"We did not ruin Mr. Bowers' career. He was the only one who could do that," Myers said. "We did everything possible to help Mr. Bowers overcome his problems, but there was no cooperation." She said she could not elaborate.
Myers said she has not gone public with details of Bowers' dismissal because it's still in litigation, and out of deference to him.
Myers denied she's obsessed with power. "C'mon, what power is there, being mayor of Smithsburg?" she asked. "If you do the job right, it's hard work - satisfying work. I like doing things for my town. I don't do it for the money, that's for sure."
The mayor makes $2,000 a year.
Myers said there is danger in giving department heads free rein. "We're talking about use of taxpayer dollars ... All departments follow established guidelines as required by the elected body," she said.
"If I'd been sitting on him (Bowers) all the time like he says, many things that took place probably never would have happened. When problems surfaced, by the request of the council he was monitored very carefully ... Before that he had free rein."
Myers, a member of the Washington County Ethics Commission, said the town decided against forming one because it's hard to seat a totally impartial panel in a small town.
Anyone who feels there has been an ethics violation in town can go to the state, Myers said.