You can put her in the bucket if you must. Just keep it heated and put some decorations to make it feel homey. I wouldn't put her in the breeder net seeing how she's still in the 20 gallon, she'll establish her territory.
What you must do is leave her in her own tank/bucket for 2 days, after that change the decorations in the tank, move things around. After one day or so, the fish in the tank will establish their territories. After that add your girl back in, see if she's her nipping mood, if that doesn't work she'll have to live alone, sorry. :/
Tanks come fairly cheap to be honest, what I've noticed is that the bigger the tank the cheaper it is in general. My 2 gallon Fluval Spec was more expensive than my 10 gallon. So consider buying a bigger tank, look around in all of your LPS and LFS. I found my 10 gallon for $37 at PetSmart which is pretty far away. . . So yeah try to think big!
If not, you can always buy those Kritter Keepers, they're pretty good homes if you buy the large sized ones. They're pretty sturdy too, and aren't too costly.