@Derek *********
So, your girlfriend got the blue housebook She first has to register the house in the TM30 Online System. She will receive a login-ID and a password. She will be asked by the system to change the password.
After this is done, your girlfriend can report your arrival at her house in the TM30 online system - as having arrived at this accomodation.
You, the foreigner, usually don't register the house in the system by yourself, as you would need the blue housebook and the data it contains to do so.
However, if your girlfriend gives you the login-ID and the password, you can register every of your arrivals by yourself.
Instead of this proceedings, the two of you could also visit Immigration, together with her blue housebook and her Thai ID card and you with your passport, and register the TM30 directly at the Immigration office