Echoing Animularisen's sentiment, your gf has to be certain that this is what she wants...she has to be enthused about it. If not, she won't be relaxed and aroused enough for a pleasurable experience. So be certain that she isn't just going along to please you, that this is something she's genuinely excited to try.
Have you tried anal fingering? If you haven't yet played with her anus, she doesn't yet know whether or not she's interested in trying anal sex; that's like saying you want to be a doctor when you've never cracked open a biology book. So start out with anal massage, using your finger or a small vibe (clit vibrators work well for this, but only if they're plastic/silicone, so you can disinfect it afterwards; otherwise, put a condom over it). Sometime when you're giving her oral, lube up your finger (some ideas for good anal lubes: Anal Lube, Probe Classic, Maximus) and very slowly insert it into her anus and leave it there (don't move it back and forth), and if she isn't at all sore afterwards, the next time you can try two fingers, and so on. A caveat:
She must tell you if there is even the slightest bit of pain at any point; if there is, stop immediately and try again another day. The preceding warning goes for any and every anal activity. Another idea is to purchase a small/beginner's anal plug and use it the same way. (I sometimes use a small one whenever I'm playing with my vibe and, wow!, the orgasms are incredible

) You can graduate to something a bit larger (plugs often come in small, medium, and large) whenever she feels ready.
I think the new vibrating plugs, Rump Shakers, look like a lot of fun

If you get one of those, let me know how she likes it.
Anal dilation is something you don't want to rush because overdilating an anus that isn't properly prepared
can permanently damage the anal sphincters. Something else to keep in mind is that rectal tissue is very delicate, unlike vaginal tissue, so thrusting should always be gentle, entry should be done slowly, and you should always use generous amounts of lube (you can get away with less if you use one of the lubes I mentioned previously--they're thicker than normal).
If she doesn't enjoy anal play, she's obviously not going to enjoy anal sex, so please respect her feelings and encourage her to be 100% honest when discussing it. Anal sex isn't for everyone. You don't want to overdo the anal play (or anal sex), either. The sphincter muscles need time to recup.
Be safe and have fun!