This is a standard problem, not just in CA. Assuming you don't need CA qualification, which is something for your lawyer not your bank to figure out, give them

This is a standard problem, not just in CA. Assuming you don't need CA qualification, which is something for your lawyer not your bank to figure out, give them a letter stating that you have no employees in the state and as such don't require CA qualification. That and some persistence should get you what you want.