As a college professor, frequent traveller, and someone who spent six years of my life commuting to a job in a different California metro area than the one I lived in, I second the previous posters. This is both insane and not worth it. If you want to go back to school to get a Masters, either apply to a program closer to you (surely there are some in the LA area) or commit to living in the East Bay for at least part of the week. Presuming you're attending a quality MS program, you are going to get as much or more out of the time you spend outside the classroom than in, and what you're proposing has you spending as much or more time in transit than anything else. And that's setting aside the realities of both LAX and the Bay Area (neither are known for their reliability) or the commute situation at both.

In all seriousness, anyone contemplating a commute anything like this should look into (semi)-private options like Surf air, but again, that just makes it somewhat less painful and even more expensive--but still far from worth it IMHO.

ETA: Finally, in case you really don't want to face reality and actually try this, WN is the only option--you will need their flexibility of choice of Bay Area/LA Basin airports for the mornings when fog shuts down one or more options and you have to get to class. You also should get to know the various GAs so they can give you a heads up when, e.g., the prior night's flight was late and crew isn't going to have their minimum in time for the first flight out, etc., etc. Even folks who do this as a weekly commute know you're going to be late with some regularity. I do it with *far* less frequency and still walk myself to WN from AS when I absolutely have to get to the Bay Area and AS has dropped the ball.