Not from Ohio, but I'm just north in MI. We have the Great Lakes Bowfishing Championship...200 teams and 2 days of shooting. If your willing to drive its a lot of fun.
We also have BAM (Bowfishing association of Michigan) that puts on several smaller tournaments. There might be some sort of group like that down in Ohio that puts on tournaments.
Last summer was my first year shooting in tourneys and it was a blast. The competition aspect of it adds a new kind of fun.
The GLBC can be as competitive as you want, or as relaxed as you want.
You really don't have a chance to win against the airboat rigs out there shooting 3 ton of fish in a weekend, but they pay out to the top 20 and with some work, that's doable. I think we got somewhere around 50th last year as our first time. Lots of easy access, and they provide lodging and meals if you want. It's all fairly reasonably priced as well.