Howdy,
If you just want to keep n number of copies rotate back them up in some more generic fashion. Then rotate them before the mysql dump. It'd look something like this below.
rm dbname.bz.4
mv dbname.bz.3 dbname.bz.4
mv dbname.bz.2 dbname.bz.3
mv dbname.bz.1 dbname.bz.2
mv dbname.bz dbname.bz.1
Now run your backup!
The dates are still no the file status. If you ever wanted to get them ls -l would flush it out.
As for partial backups, I like a simple 1 file = 1 good backup. But that's my personal opinion.
Also I don't backup on server, I scp the files off location as soon as they're backed up.
You're welcome to use anything I've posted, if you mention my name send me link.