Does he sleep in bed with her when she is not at your house? And I'm just going to go ahead and assume that the only thing potentially going on in the bed while he's there (if you were all to be in the same bed) is sleeping, because if not the answer would be obvious.
I think you have good intentions at heart for sure, but I also think that its inappropriate for a mother to let her child sleep in bed with her (kinda new) boyfriend. If you guys had been together since he was born maybe, or if you guys were at least married maybe, but its hard enough introducing a new person/possible father figure into a child's life in the first place, let alone showing the child that this man can sleep in the same bed as him and mommy.
Also, does your gf still talk to the boy's father? Is the father still a part of the boy's life? I would imagine that if so, he would be very unaccepting of another man sleeping in bed with his child. Your gf says she doesn't want the boy getting the wrong impression, and it is somewhat about that, but I think its even more about other people getting the wrong impression. I can only imagine what my mom would say if I left DH and got into another relationship, and then let my son sleep in bed with the new guy and me.
Just to put it into perspective.
What I'm trying to say, in conclusion, is that I don't think its a subject that needs to be pushed. I think you're kinda stepping over your boundaries here. If she says no, leave her alone about it (IMHO). It doesn't mean she doesn't love or trust you, it just means she's being a cautious and protective parent, which is what a good parent does, and she doesn't want to risk doing the wrong thing.