Going out to play with friends, is it wrong to mention AA gas fee?

You did the right thing, but one thing, you should have told him earlier that the gas bill was AA.

At first, she thought that you offered to drive without her paying for it. She was preconceived, and then she heard you say AA, so she reacted so much.

There are only two ways: 1, don't go for the time being, and find a chance to explain it later; 2. Talk to her directly and understand with emotion. If she is sensible enough, she can understand you.