There are buses running all over the city but I would suggest texting a Lyft or Uber driver to the rental car lot.
I would use Lyft or a taxi. There is a Avis location 2 miles away from the union station.
Or take the fly away from union station
I agree with Hank. Just take a cab or Uber to Avis. No need to go to the terminal just to get the shuttle if you are already in L.A. If you are arriving on a flight to LAX then follow the signs to the Avis shuttle.
If you don't want to take several city buses, then an airport shuttle or taxi/Uber. The taxi could drop you directly at Avis. Otherwise you have to catch the Avis bus in the terminal.
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