Lost a crab pot, need advice on how to get it back.

This morning one of my crab pots went overboard without buoys attached at about a depth of 80-90 feet. I know exactly where it is, and while I can just buy a new one, I've decided to challenge myself with recovering it. Right now the thought is to drop a rope with a claw on it in the general area and hope I snag it as I float by. Curious if anyone here has any advice or ideas on how else I could go about recovering it.