If you are relying on this person financially, like if you 2 share a place together, I would definitely be a bit concerned over this one and I could see your hesitation in not entering the other woman, if that is the case you should definitely have her bag packed or yours incase this goes south.
Generally speaking, if you are showing less sexual interest in your girl, then this new one shows up and your all over her its going to deeply offend your girlfriend, I would let her lead.
This might also be a precursor to her asking to have a train ran on her, "OK youve had your fun, time to have mine" or if this chick also has a boyfriend and they want to swing, could be bad.
Overall though if you plan to stay in this relationship I'd say this is a bad idea.