I am looking to do some bouldering in Moab area.

Any ideas for free camping, where I can just throw down a bivvy hidden from view,

Or is BLM land cheapest?

Where are some good Bouldering Areas?

Unglamorous but free camping can be had in the Amasa Back overflow parking lot. Don't pitch a tent, it's just a gravel parking lot. I've slept here many times.