Long ago I installed git on BlueHost... but then was largely thwarted from using ti because of the non-interactive shell, don't know if it'd work with VersionPress or not.

see:
http://willjackson.org/blog/installing-git-bluehost-shared-hosting
and
http://www.bluehostforum.com/showthread.php?20304-Bluehost-Solution-to-the-Git-PATH-issue-when-using-a-non-interactive-shell

Regardless, the better solution really is to give up on bargain basement shared hosting. Suffering shared hosting to save less than $100/year seems crazy in hindsight for all but the most unimportant of sites.