I figured out how to accomplish this for both prompts (bash and mysql). I've edited my .bash_profile so that it will make this change permanent, so to speak.
To make the mysql prompt change permanent, I need to edit the my.cnf file, which is in /etc/mysql. The file is read-only, though, and if I try to chmod it, it says 'Operation not permitted.'
I guess that's probably just a limitation I have to deal with, right?