I took physics and calculus and other such advanced courses in high school, and graduated never having heard of Bayes' Theorem.

Must be a problem of the American school system, I suppose.

I didn't learn about it in university, either–granted, I was in 'Statistics for Nursing', it's possible that the 'Statistics for Engineering' syllabus included it.

Did they teach you about conditional probability? Usually Bayes' theorem is introduced right after the definition of conditional probability.