Do you have access to a shell at your host? If so, you can do it pretty easily. If not, I don’t know of an automatic backup plugin for bbPress.
Yeah, I have shell access…
I had a shell script before to back up my whole schema; but I just want to back up the bbpress schema now, not the wordpress schema.
It’s great that you have shell access. You can backup all the files with something like rsync, and you can use a shell script to backup the database tables you want. Since there are no wildcards in mysqldump, you will need to explicitly name all the tables in your installation; just separate them with spaces.
You can put something like this into a bash script and run it daily (or whenever) from cron:
mysqldump --add-drop-table -h host -u user -p password dbname
( bb_forums
bb_meta
bb_posts
bb_tagged
bb_tags
bb_terms
bb_term_relationships
bb_term_taxonomy
bb_topics
bb_topicmeta
bb_users
bb_usermeta ) | bzip2 -c | bbpress.bak.sql.bz2
You would have to consider putting the password into the script and hiding that from prying eyes. Alternatively, you could create a user with limited privileges and no password, and use that in the backup script.
You should also verify the table prefix, and that those are all your bbPress tables. I think there are different tables for different bbPress versions.
Good luck.