I asked the question on Bluegrasspreps.com, what are these "bowl games" in KY about during weeks 1 and 2. This is the answer I received:
Generally bowl games are in Week 1 or Week 2...that isn't any requirement of the KHSAA as far as I know of, but traditionally some of the long-standing bowls like the Montgomery County Recreation Bowl were at the beginning of the season to kind of "start the season off with a bang."
Most of the bowl games are just played at a regular high school field. The Rafferty's Bowl played at WKU and the Forcht Bank Bowl which is usually played Campbellsville University are the only two that pop to my mind as played on a college field. The Skyline Chili Crosstown Showdown was created to be played exclusively at UC's Nippert Stadium, but that's turned into a kinda obnoxious season-long series of games.
Sponsorship is generally the biggest part of the equation. That's how teams encourage out-of-town programs to travel for games - by having sponsorships so they can offer stipends to participating teams. And the unique/out of the ordinary match-ups are intended to increase spectator attendance for the games, which they generally charge a few bucks more to get into. No idea how the gate is split among the teams, but I'd assume that's a different scenario for each of the different bowls.