Let’s clear the air. A California burrito does not contain rice. Repeat: no rice. That’s a Mission-style burrito from San Francisco, which is a different, equally valid beast. Rice here would be a filler, a distraction from the holy trinity of meat, fries, and guac.
Also, no beans (usually). If you see black beans or refried beans inside, you’re ordering a hybrid. It’s fine, but it’s not a classic California. Keep it simple, keep it clean, keep it crispy.