ASA Sailing School and Charter Boat Services Southern California - Marina del Rey, Southern California (CA)
These guys are out of Marina Del Rey about 10 mins from LAX by taxi.
I've chartered from them a couple of times (last time a nice Beneteau First 38)
Catalina is a days sail so it should be possible provided the weather holds up.
Both times I've gone in March and the weather was good. Catalina was not busy (most californians think it's still winter) although I was wearing shorts all the time.
They changed owners on my last trip, but I suspect it's for the good.