I don't know if there is really an ABA bubble it is more of a California law school tuition bubble many ABA law schools outside of California have very reasonable tuition rates I.E. Florida International Law School, CUNY, South Dakota, North Dakota, all are $10,000 or less per year in tuition.
However, California law schools can charge as much as they do because people keep enrolling and many students nationwide want to live in California so the tuition keeps getting hiked up. With that knowledge perhaps to graduate with an ABA degree you might want to consider a law school with cheaper tuition rates outside of California. I don't know if that is a possibility, but I think having an ABA degree is better than a CBA one all things considered.
Right or wrong there will be doors closed to you without an ABA degree it doesn't mean you can't succeed, but many firms, agencies, etc will only consider ABA grads at a minimum. On top of that if you go into private practice or start your own firm potential clients will look you up and if they see you went to an unaccredited school they probably won't choose you. I personally know the educational difference is minimal, but when selecting an attorney people like hear the word accredited. On top of that if your a Solo you will be competing for clients and other attorneys from ABA schools to help themselves may say oh she went to an unaccredited school. Kind of shady and certainly many lawyers do not do that, but it is a competitive business and something to consider.
By analogy if you were choosing a doctor to perform you surgery and you heard one of them went to an unaccredited Medical School you would be more hesitant to choose them over other doctors that went to an accredited law school. Does that mean you can't succeed from a CBA school? Absolutely not the Mayor of L.A graduated from a law school that was not even CBA accredited and he is bossing around Harvard Grads.
In the end since your halfway down the ABA path I think your better off staying there, but I am just some guy anonymously posting on the internet. Also on the flip-side when you pass the bar whether from a CBA school or ABA school you are a lawyer in California with the same rights, responsibilities, etc that a California Lawyer from Harvard has.