My band is looking to broaden our popularity in the coming months, and we are contemplating the possibility of hiring a booking agent. How would we go about finding one, and how would we know if they can be trusted to both do their job and not screw us over?

And once we find one, how would we go about applying? Would we use a press kit?
"If you're going to try, go all the way. Otherwise don't even start..."
Charles Bukowski
My band haven't done anything like this yet. But my advice would be speak to other bands and see who they recomend you.
my band's "booking agent" is our general manager, whos real job is sumthing like a builder. i dont know how your band is, but some can get away with just haveing a friend that has alot of conections in the industry, such as a past musician or maybe someone who owns a bar or something like that. also if you're looking on expanding your popularity, make a street team. get a team of close friends/big fans to go out and mention your band to people and get them to go to ur next show or whatever, it works a treat. but as far as getting a propper booking agent i havnt a clue. but a friend with conections is less likely to rip you off and more likely to do it for free.