If you want your girlfriend to give up the back door, you have to introduce it slowly into your relationship.
One thing I like to do is during the 69 position with her on top. As I'm giving her oral, I lick my middle finger and place it against her anus and apply a slight pressure... I do NOT penetrate. There is always a slight reflex action by the woman, but since I do not penetrate they don't get scared and they think the sensation feels good. I'll do the same thing during cowgirl.
The key is not to penetrate the first few times you do this. She feels safe with you and likes the sensation. After a while, just like everything else in life, you begin to escalate by making shallow penetration. Each time you have sex, you can go just a little farther. The key is to gain her trust that you wont hurt her, humiliate her or embarass her. Then also make her believe that you are playing with her anus to stimulate her, not yourself. Eventually she'll ask you for anal intercourse, but if she thinks you want it for your pleasure then you can forget it ever happening.