We flew into and out of LAX. There was lots of transportation between LAX and DL. A lot of people use Super Shuttle, we saw some cabs, and limos. Some hotels have their own shuttle. We were on the Airport Bus, but I'd say only use that as a last option. It was okay, (got us to DL, which was the important thing!) but we waited longer than anyone else for our pickup at the airport.
BTW - on our way from LAX - DL the trip took about half an hour. On the return trip, in morning rush hour, it took us twice that long.