The "Burbank Airport" stop as it's still referred to in the timetables is across the street from the airport entrance. Short walk from the terminal past the on-airport rental cars then across the street.

Unfortunately, the economy has caused Southwest to cut and rearrange flights, and Metrolink to cut runs, so the N.Cal.-LA commute is no longer convenient via the train connection at Burbank. Used to be an hour on the plane, 20 minutes downtown, and your train ticket was a transfer to any local transit (downtown bus/shuttle or subway) at Union. The connections no longer work unless you get the first flight in the morning (crack of dawn or earlier) because there's a big hole in Metrolink's and Amtrak's inbound service there after about 9 AM.

BTW, those shelters look pretty but they don't produce much shade...