Very Cool, But Not For Everyone
We stayed here two nights and really liked it. There are a lot of travelers and some locals who come to the beach for the day, to look at the art of just to hang out, but overnight it gets pretty quiet. The first night there was only us and a bikepacker in a tent, and the second night there was a car camper that left early in the morning. Some ATV people riding around the sand also but they weren't too bad. There's also a guy in a nice small trailer down on the beach who looks like he's been there a while, but his site is nice and clean.
It's easy not to get stuck in the sand if you stay in the upper area. We had no problems in our 26ft class c. If you drive down to the beach just watch for the soft sand and stay on the hard packed parts.
The town and the beach are just so... interesting. The artists are taking over the nearly abandoned town and it's really neat to see. Curious to see what happens to the town of Bombay Beach in the long run. Very interesting history, both the sea itself and the towns around it. Lots of documentaries about it on YouTube if you're interested.
There's BLM land here but I think the part you can stay on is owned by IID (Imperial Irrigation District). Not sure about this, but anyway I don't think camping here is a problem.
Good cell reception and weather in mid November. We would have left if it was windy to avoid breathing in the particulates.