I like improvising and then cherry picking the stuff I like. Once I have it I really don't want to keep the garbage that's left over. Is there a way to permanently condense a bunch of fragments into its own region?

Sure, just edit the longer Regions in the Tracks area into pieces as you want them. Check out video #20 etc in the course linked above.. If you mean permanently deleting the excess audio after you've done that, well, some DAWs have commands for that but I don't think GarageBand does -- but I wouldn't worry too mach about that, audio files are not that big considering the capacity of modern HDs. And you could always Bounce (Export) the edited Region(s) down to separate WAV (audio) files..

I meant the latter. I always avoid bouncing because I was told that there's a drop in sound quality. Is that true?

Back in the analog era (i.e. with analog tape) bouncing down added a generation of noise and signal quality loss, but in the digital world at 24-bit resolution there's no need to worry about loss of sound quality when bouncing inside the box, as long as the signal stays in the digital domain.