On my playthrough, I decided to go ahead and choose to neither collar nor tattoo Bizzy. After rescuing Dizzy from Paragon and bringing her to Bizzy's studio, I go through Dizzy's options and find that, for some reason, I can give her a tattoo while Bizzy doesn't have one at all.
Probably not a bug, but I find this a very weird thing to have possible when you haven't done such to Bizzy.
Probably not a bug, but I find this a very weird thing to have possible when you haven't done such to Bizzy.