Hi neighbor and welcome to TBN and the forum. I put a Rankin tooth bar( Yakima, WA) on my bucket. It came with a "tighten the bolt down onto the lip of the bucket" attachment method. I simply drilled four holes thru the bucket - ran grade 8 bolts thru the tooth bar & bucket and made an attachment system that is guaranteed not to fall off. Tooth bar addition to the bucket helps with back dragging, busting clods, smoothing all sorts of furrows and mistakes I generally make.
You should also check out a Piranha tooth bar. Quite a bit different than the standard tooth bar and has some very unique advantages - raking, much finer back dragging etc.