Where can I find an evening Chinese class or teacher/mentor in Los Angeles?

You can post an ad on Craig's list or post in the CSSA (Chinese Scholars and Students Association) forums of UCLA and USC. You can Google for the URL. You don't have to be a CSSA member to post there. You might even get the lessons for free because a Chinese student want to exchange language lessons.

There are a ton of language-specific meetup groups, which are for people who want an opportunity to practice the language. Join a couple, go to a couple of meetings, and ask around there. I'm sure you could find someone interested in tutoring, or someone who has another friend who is interested. Also agree with wcmf's suggestions above.

Seconding the language exchange idea, perhaps a simple CL ad would work, it is worth a shot. Or a hand-printed flyer / ad posted in a chinese grocery store (haven't lived in WLA for some time, but why not at the 99 Ranch Market if you frequent one?) Way back in the day I took Mandarin at Santa Monica City College, and they had a convenient Saturday schedule. Looking up http://www.smc.edu it's comical that there's nothing online, just a PDF. Anyway the courses were well done, met a lot of interesting people, and may provide the structure / discipline of a 'course of study' that you may prefer instead.