It probably means that she always believed in Adrian, and always defended him verbally, which caused her to lose many, many friends. To burn the bridge means something like losing someone's friendship permanently.

You cross a bridge from A to B, then you burn the bridge behind you so that you can't reach A any longer even if you wanted to. (Burning a bridge = tearing up a contract, slamming a door behind you with finality, yelling at your employer so that he would never think of hiring you again, completely neglecting a relationship to the point where it's unrecoverable. It's doing something that makes it impossible to return to a previous thing.) In other words, you can't reach the other thing (A) anymore. Liz only has B and can only depend on B.

"burned a lot of bridges" means to destroy or damage your reputation because of your bad behaviour, or to in general do things which will harm your future. A rookie is someone who is still new and inexperienced at a job. "Liz's faith in Adrian Wall had burned a lot of bridges when she was a rookie." is a strange sentence. What it probably means is that when Liz was new at her job her faith in Adrian Wall had been damaged or destroyed. In short, she now longer trusted him.