BFA/MA in screenwriting

It's good fun, but a complete and utter waste of time and money. So just like many degrees.

Major in a field that will make a living, minor in what you want to do. If you catch a break and become known, wonderful. If not, you're not stuck living on Ramen Noodles and drooling over bologna.
There's nothing wrong with aiming for the stars, but be smart enough to carry a parachute for the fall that may happen.

It does sound like incredible good fun, but as was stated before, it is not a degree you can readily make a living off of. Even what I am majoring in now won't assure me a job, and I'm probably going into teaching with a History degree. Major in the something you're good at that is most likely to get you work. Not that you should put aside screenwriting, I certainly haven't, but getting hired as a writer or getting something sold is like pulling teeth, often times very painful. And do you have any idea how much those masters credits cost? You'll definitely go holy shit! So anyway, I think what everybody is saying is keep writing, but get a masters in something that will possibly make money for you.