There's nothing in the rules to preclude what you're saying. As long as your girlfriend has the requisite 12 months on JA then that should be fine.
If she isn't making the BTWEA application hereself, then it could cause difficulties if she continued on her JA claim and became a company director, as the Department
would be questioning whether she was in fact available for and seeking work.
The other way to go about it if she doesn't meet the requirements of the scheme would be for her to go onto your claim as a qualified adult, and for her to continue to sign on for credits.
However, I don't see why you both wouldn't be able to make an application for BTWEA. The only potential issue that I could forsee would be the requirement for the businesss to be a new one, but if you were both simultaneously setting up the business, then that shouldn't be a problem. It might not be a bad idea however just to give the enterprise officer in your local office a call, or perhaps contact someone like the Irish National Organisation on the Unemployed to run it by them.