Im flying F to LAX soon and will also be jumping on the Flyaway Bus to Union Station. The Flyaway website doesnt really say where to buy tickets so i asked the same question on Tripadvisor and got 2 answers. 1 was you buy the ticket from the driver & the other was you buy it once your arrive at Union Station which i thought was a bit odd, but was told you cant buy it inside LAX. Sorry that really isnt much help to you is it.