I wouldn't bank anything on grants. The state is bankrupt and you're gambling. Not sure what your age is. I'll assume 22. I completely agree with leekohler about just going balls out (sorry

) and going for it. You only live once and you can recoup this mistake in your later years. Kidding
But where are you in your education? If I've missed that, my apologies. You've been to LA it sounds like. Getting around on a motor bike is doable though a pain for that to always be your vehicle. **** is expensive here and like dmr suggested, go the roomie route for sure if you can. Not hard to do.
You want a bank account of 5-10k to move imo. Jobs are tight here and I wouldn't personally move without a job. Maybe you can visit your cousin and apply?
You could just go with the clothes on your back but it sounds like you're being cautious which I think is good. Any idea where in LA you were that made you think, I want to move here? That will help. Hundreds of miles and a million suggestions. I'd suggest that you keep this as a goal, save your money and graduate where you are and then move to save all the in state tuition BS. Get your degree and then split.