For $39+Tip, I used Supershuttle to make this same exact trip after a flight to LGB on B6. Although I do have some bad Supershuttle stories, in this instance I would recommend it.

LGB is a small enough airport so it was easy to find the pick-up point, and the Supershuttle van that was there to pick us up was waiting for us on our arrival. The driver even called me to let me know he was there and I got a message when I turned my phone on right after landing. My sense is most people who use Supershuttle are headed into L.A., so while there was another couple in the van, we were dropped off first, since LAX is on the way to downtown.