This is tricky. Are you in a common law relationship? For a sponsor, I think it is important to have a strong relationship with the applicant (parents, wife, etc). You and your girlfriend could theoretically breakup and then what? There is no legally documented relationship here unless as I said earlier, you are in a common law relationship.
If you are an American citizen, why don't you arrange for an educational loan and your girlfriend could pay that instead of directly supporting you if she wants to sponsor you? US student loans can be used to study abroad particularly Canada, UK etc. I am not sure exactly which loans offer this benefit but you could easily find that out.
Also, if you are an American or US Permanent Resident, you can apply for a study permit at any border crossing. Just FYI.
This is just my opinion. Hopefully others can shed more light on the issue.