From UCLA either the 405N to 101E to 134E exit Hollywood Way...that is 40 minutes to airport with no traffic

or alternate route is 405S to 10E to 110N to 5N exit Hollywood Way (or where is say Burbank Airport) - thats prob like 45 min no traffic

Either route without traffic isnt bad.

check www.sigalert.com and look at those freeways before you leave to see what traffic is like

OR OR OR
East on Sunset to Coldwater Canyon (street right by Beverly Hills Hotel), go north on Coldwater Canyon and that will pop you out on the Valley side and you can get on 101E (or South, whatev its called there) and take that to 134E to Hollywood Way...this route is pretty easy barring any crazy traffic delays...think 45 minutes for this one too, maybe less