First came the unhelpful bank tellers. Then the unexplained monthly fees. Then the fumbled mortgage application.

When Richard X. Bove encountered this string of bad experiences at his Wells Fargo branch in suburban Tampa, he didn’t sit quietly and fume like other Americans who have grown frustrated with their banks. He began by moving his business to a bank down the street — then he used his platform as one of the nation’s most outspoken bank analysts to tell his story to thousands of clients...