As someone that spends almost everyday on BB, I'd pass on the swimming part. Very weedy and gross. Towards the dam at the back I guess its a little better. But overall I'd pass.
There's three beaches in town. All free. Area is great because its far enough from downtown, but close enough to walk.
And yes, there is a bridge you'd have to be able to fit under.
Back Bay has the
best bass fishing on the entire lake though.
PM me if you want anymore info.