I managed to convince mine back in the days for a bit of anal. I found that joking and not adding any pressure on her worked well. Maybe tap into it bit by bit, like one night try a bit of rimming action and then go from there on the future occasions. You also wanna get some lubrication and if at any time she is not comfortable then just be fine with it and maybe try again at a later date. If your girlfriend is worried that is only gonna make it more difficult.
Hey it worked for me and it wasnt just the once I got to do it either!! Good luck- I know what it's like when you're gagging for it!!