Elisa,
You don't say how long you've been in your relationship and how committed you are to it ? I'm not sure if I agree with Tinkerbell on the point of facial hair ! Really you have the right to alter your presentation as a guy, you could say the beard is giving you a skin problem and need to shave it off !
If you're having problems presenting yourself as a guy with your GF, maybe your relationship will get more onesided as it progresses, as for CDing issues you are probably going to be closeted forever !
At the stage you're at tell your GF staight about your needs, you will be happier in the long run ! Please believe me on that one !!
Reading your OP again, you don't say if your GF knows about your dressing ! So do you know what thoughts she has on CDing at all ?
Vickie' I had two consecutive GFs that were OK with my CDing so in my case the figure was two out of three !!