I was wondering if the shuttle bus runs 24/7 these days. and how frequent? in the very early in the morning like 4am.

They run every 5 to 10 minutes 24/7 Unless traffic at the airport is bad due to construction, if so please be patient they are working hard to get you to your airline or Rental Center. Welcome to Avis LAX

You have to consider they're 7 terminal but shuttle pick up on 5 location designated for car rental. Once we pick up on number one it could be busy or not then we go to the next one terminal 2,3,5, and seven. So if you want tho BE pick up FIRST then go to 2b which is the first pick up that we go thru until the last terminal which is 7... Shuttle never end it continue to pick up 24/7. With 8 buses.