I would say that it wouldn't be your place to tell her she has OCD; really, only a trained licensed psychiatrist or psychologist can diagnose that. Maybe a LCSW and LPC could also diagnose that. As much as we would like to help our loved ones with a condition we think they have, the best approach isn't to play the diagnoser but to actually just describe their symptoms as you see it (no diagnosis, just the symptoms you observe, such as the excessive hand washing) and how it is affecting your relationship with them. Additionally, you can perhaps add that because their behaviors or symptoms are affecting the relationship you hold together, maybe therapy might help. If she's put off by individual therapy, you can always try couples therapy to show her that you are willing to work with her and to hopefully have the licensed couples therapist see what is going on and perhaps offer a diagnosis for her at that time. You can also ask her if she's ever been diagnosed with anything related to the symptoms and behaviors she is showing you. It may be that she is aware she has it, or it may be that she isn't ready to face what she has. Either way, openly communicating without labeling or diagnosing might feel less threatening for her. You know your GF best, so approach her in whatever style you guys enjoy communicating, but without the labels or diagnoses.

You can be gentle and say something like, "Hey sweetie (or whatever pet name you have for her), I noticed that you do this and say that, and I was wondering if we could discuss this together?" See what she says after that. If she sounds defensive, then tell her that you care and don't mean to be defensive, but that you'd like to see her less anxious and more happy when you two are together, and for herself as well when she is alone. You can reiterate that you're bringing this up because you care about her. See what she says. If she's open, she'll explain why. If she's closed, she may say that she doesn't want to talk about it. If she's closed, you can always say something gentle like, I can wait to talk about this at another time, when you're ready, but I am really concerned and care about you. See what she says. Be patient and wait a day or a week. If nothing is brought up from her, then you bring it up again and request to talk again. Keep trying and maybe add one more request to see a couples therapist or for her to see an individual therapist (though the individual therapist thing might come across as harsh to her, so try the couples therapy suggestion first).

You know how the flow might go, since you know your GF best. I hope these tips help. You might have better tips from others.