Thanks for the suggestions, everyone!
I rode it today and exited on College Park Dr. as suggested. Going home I searched for an access onto Atherton, but instead found a slightly rocky and disused, but rather picturesque way onto the opposite side of the SGRT at Via Del Rio St. - which is a side street just off the end of Atherton. It gets onto the west side of the river, and the north is blocked off by rocks and bushes, and looks a bit dangerous, so the only way is to ride south to College Park Dr. Otherwise, yep, I've found a pretty decent way to class.
For any other CSULB students thinking about commuting by bike, be advised the parking and traffic are supposed to be the worst ever this semester - so it's a great idea to pedal there, as well as serving as a warning that there's going to be a bunch of freshmen who are looking more at the buildings and streets than the cyclists or people.
I'm thinking riding west onto campus on Anaheim is the better idea, it looks like it has much less vehicle traffic.