A new host! That seems like a rediculous constraint.
BTW, with bbPress 2.0 plugin (site wide bbPress), it does not use a separate DB or separate tables. It uses custom WP Posts inside the WP dB.
As far as I can tell, BuddyPress does not use bbPress 2.0 plugin for group forums, instead, it uses an internal version of bbPress 1.x. It also uses separate dB tables.
If you are using bp 1.5 with group forums, you should have a set of db tables with the prefix that includes bb_. You should also have a file called bb-config.php
The file bb-config.php has settings for the bbPress (1.x) database name, user, and password, and table prefix. I’ve not tested this but conceivably you could create a separate db for your bbpress tables and modify the config file accordingly.
It does not appear that the buddypress tables themselves are so easily separable.
I would strongly recommend that you not try separating the databases until you have successfully done it in a test environment. Also, as always, do a site and dB backup before you do anything just in case.
joe