It's very common to have a by foot quote for painting which usually includes the bottom paint. There may be a minimum charge or different price ranges depending on the over all length. That price usually assumes the boat is in the boat yard's area, blocked and ready to paint. Haul out fees, launch fees, etc will often be in addition. Many small lake marainas have lift deviced designed to lift the boat off the trailer and that is included in the price. I usually did the bottom paint myself as it can be very expensive to have it done professionally. However, the trailer situation may make the impossible to easily do yourself. I've seen a few boatyards that charge something like $20-$30/foot for boats in that range, but this is something that can vary incredibly from boatyard to boatyard.

The thing to do is call around to boatyards with small boats and just tell them your situation - a boat on a trailer needeing a new bottom paint job and get a few estimates. It helps if you know what kind of paint is on it now as certain kinds of bottom paints don't work well over others.