You're talking about a drag bike, 0 to 20, and it only has to make one run or just a few runs to win the money, right? Buy the cheapest geared used hub motor you can find, get the most voltage you can afford even if it's lead acid batteries, and wire it up w/ an on-off switch and a kill button, no controller. Controllers are for sissies w/ a drag bike.
Ideally you'd want a 24V motor and about 100 volts from the battery. More would be even better. Might want to drill some holes in the motor casing to hopefully get some of the heat out. I would think that for such a short run, there is no such thing as too much voltage. You can buy 8, 12v 5AH sealed lead acid batteries on the site below for less than $100, and that's w/ shipping included. Mount them toward the front of the bike to keep the front wheel on the ground at the start. That setup gives you 96 volts and less than 30 lbs of weight. Increase your budget a little and you could get 150-200 volts, but the extra weight gets a little tricky on a bike.
https://www.batterysharks.com/12-Volt-SLA-Batteries-s/1213.htm
If you have a lot of time on your hands you could take about half the wire off the armature windings and get that motor voltage reeeeely low. Easier to just add more juice though. Forget the idea of 0 to 20. With multiple bikes, everyone is going to have their own idea of what "20" actually is. Make it from a standing start to maybe 50 yards, something like that. You'll need someone to drop the flag at the start, and having someone else make a video of the race would be nice :]
