On my last stay there on May 11th the shuttle schedule was
1) Westin
2) Holiday Inn
3) IIRC a Quality Inn nearby
Shuttle frequency: every 10-15 minutes
Time from the Westin via the other 2 hotes to LAX: about 15-20 minutes. If you catch one that has a complete long-haul airline crew onboard (as happened to me on the 5:30 a.m. one to the airport) you'll probably have to wait for the next one.