Just bedroom practice and direct recording from the amp's output to my soundcard's input. It's a Line 6 30 watt Spider IV.
I've heard that you don't need a bass amp as long as you don't get too loud.
Also, if I'm recording, it's bypassing the speaker directly, so is that ok or are the electronics in a bass amp different than in a guitar amp and a guitar amp won't be able to handle the signal?
No risk in doing so. If you hear the speaker farting out then just lower the bass and/or volume.