The Ancient One recognises that Strange is meant to be "the best of us" and after having been told Strange gave it up willingly he must have had a reason for it. Therefore, she is trusting in Strange, and so Bruce, that whatever is happening, is happening for a reason and gives him the Time Stone per Strange's plan.
She needn't have known what Strange's plan actually is, he could have looked forward to work out how to win or might be playing a long game with time travel or something else. She doesn't need to know the actual plan just that it's Strange's and that's enough for her to trust his judgement.
Bruce: Then, why the hell did Strange give it away?
Ancient One: What did you say?
Bruce: Strange, he gave it away. He gave it to Thanos.
Ancient One: Willingly?
Ancient One: ...Why?
Bruce: I have no idea. Maybe he made a mistake.
Ancient One: Or I did. Strange is meant to be the best of us.
Bruce: So he must have done it for a reason.
Ancient One: I fear you might be right.