most people in the general public don't know Bayes' theorem

Really? What probability do you assign to that statement being true? :D

There are national and international surveys of quantitative literacy in adults. The U.S. does reasonably well in these, but in general the level of knowledge is appalling to math teachers. See this pdf (page 118 of the pdf, the in-text page number is "Section III, 93") for the quantitative literacy questions, and the percentage of the general population attaining each level of skill. less than a fifth of the population can handle basic arithmetic operations to perform tasks like this:

One task in this level, with a difficulty value of 332, asks the reader to estimate, based on information in a news article, how many miles per day a driver covered in a sled-dog race. The respondent must know that to calculate a “ per day” rate requires the use of division. A more difficult task (355) requires the reader to select from two unit price labels to estimate the cost per ounce of creamy peanut butter. To perform this task successfully, readers may have to draw some information from prior knowledge.

People who haven't learned and retained basic arithmetic are not going to have a grasp of Bayes' theorem.