Understand that you would be concerned. Not knowing what the circumstances with the bounced checks were, we can't really say that this fact alone says this person should not run for president.
Also, don't think you can outright prevent this person from running and it wouldn't be right to spread the word among the voting parents about the checks.
This puts you in an awkward position, we know.
Can you (if you are on the board) have a conversation with this person and express your concerns? Perhaps suggest other ways this person could get involved?