Driving takes about 30-∞ minutes depending on traffic.
Public Transportation takes about 2 hours there

(WHY CAN'T THEY BUILD A RAIL LINE ALONG 405?!?!?!?!? OR AT LEAST A RAPID BUS)

A MetroRapid bus 761 serves the Getty Center directly. Check the trip planner at mta.net

Line 761 does NOT come anywhere close to LAX. It runs from Westwood north to the Valley.

I think the "rapid bus" would get stuck in the 30-∞ minute traffic, not accounting for having to physically exit the 405 to stop. All stops included, I'd imagine this would also come very close to the 2 hour mark. Also, if there were even a place to put a rail line along the 405, I think that the public would much rather desire the widening of the 405, which would likely be less expensive and benefit a greater number of people.