The hotel is not within walking distance at all of any light rail stops. You can check the route and schedule for the 24th St./Glendale bus (route 70) at Valleymetro.org. If you're willing to do some transferring, you can get that bus at 24th St. / Washington or 24th St. / Jefferson, or near the consolidated rental car facility. You could take the light rail going West towards 19th / Montebello, 2 stops from 44th St. / Washington and transfer to a Northbound route 70 bus. Or, you could take a shuttle from the terminal to the rental car facility and walk to a stop near there.

Otherwise, shuttle, taxi, or rental car from the airport will have to do.