In reply to BAdhoc:
oooh you dont need chalk? I use recycled dandruff from my beanie hat - gotta love some of the replies you get on here.
IMO a boulder bucket needs stability, so a nice base that helps stop it getting knocked over. And a very good closure system to stop chalk escaping when transporting it. Other than than that the comment about a couple of decent pockets for gear helps, enough room for tape/brushes and maybe a phone/wallet, job done. Theres a lot on the market and I've not yet found the perfect one myself. I even had a prototype made and am looking for somebody to refine it if anybody fancies the job.