From Amtrak Union Station to LAX Airport
All Amtrak trains serving Los Angeles arrive at Union Station. The best way to travel between the Amtrak station and the airport is by the FlyAway express bus. Express buses are fast and run rather frequently, and the entire journey (including all walking) takes approximately an hour. Beware that private shuttles run less frequently than the FlyAway buses do, and so you are not going to save any time by taking a shuttle despite paying at least 3 times as much as the cost of a FlyAway ride. Moreover, FlyAway buses run at all times, and they use separate "high-occupancy vehicles" lanes on freeways.
First of all, you need to get to the FlyAway stop. The stop is at Bay 9 of Patsaouras Transit Plaza, which is located immediately east of Union station (on the side of the yellow high-rise building, to the left of all the arriving trains). To get there, follow a wide pedestrian tunnel underneath the train platforms to the Transit Plaza and take an escalator up. All bus bays are numbered; Bay 9 is on the far side of the bus island. The entire walk takes 2 or 3 minutes.
Now you are at the FlyAway stop. The fare is $7. Buy a ticket at the kiosk next to the bus stop (cash only). FlyAway buses are large blue coaches properly marked as "FlyAway". Buses depart every 30 minutes on the hour and half hour from 05:00 to 01:00 and every hour on the hour from 01:00 to 05:00. Travel time from Union Station to LAX is about 45 minutes, but it may take up to an hour during rush hours on weekdays.
FlyAway buses stop at all LAX terminals. Passengers are dropped off on the "Departure" (upper) level of each terminal.
The total travel time from Union Station to LAX should be about an hour including all walking and riding the bus (about 1 hour 15 minutes if you are traveling during rush hours on weekdays). Do not forget to factor in the wait time, which is less than 30 minutes during most of the day. Typically, it is safe to have 1 hour 30 minutes to make this connection between the Amtrak station and the airport; however, you may want to allow 1 hour 45 minutes during rush hours or other busy periods.
The FlyAway service operates at all times, and so there is no last bus to miss.
If you still have any questions, feel free to email me (no phone calls please).