The Ohio River bridges along Kentucky (at least all of it that I've seen) should pose no problem unless your mast
is extremely tall. There are many locks that you would have to transit, but I don't know about timing and costs; but I THINK the locks process you through as you arrive (if they aren't already raising/lowering someone else), and I THINK the service
is paid for by tax dollars, but I'm not sure.
Tugs/barges would definitely be a concern. There are LOTS of them going both directions.
Also, after long and/or very heavy rains the Ohio can accumulate a lot of good sized trash (e.g. large tree limbs, etc.).
Another "watch out" would be shoals building up and extending out from the many horseshoe turns in the river.
I would also want to find a dock
or safe place to anchor
With care I think it could be a pleasant, relaxing journey in about a 25 to 28 foot sailboat; BUT I'd always be ready to "motor" to get out of the tugsboat/barges way.