I believe this was because the bowler is what they wore back east in the urban cities they migrated from, and probably for many, from Europe. As hats were a major purchase back then, you wore what you had until you had to buy a new one. I would imagine that people who had lived in the west for a long time viewed the bowler as a sign that a person was either new to the area or a "banker" type. While it is never mentioned in the movies directly, the type cast is clear. We think nothing of it as we grew up seeing movies with characters in westerns wearing bowlers, it was probably a focal point of prejudice by those who had been in the west long enough to have moved on from the bowler they inherited from their father.

To go with JJM's concept on mixing headgear, there was a character in the movie "Quigley Down Under" who wore a balmoral instead of the expected cowboy hat. It worked for the character.