you can call it a balloonist
Hot air balloon rides are very popular in California, as well as in the New England area. Companies that offer hot air balloon rides are: US Hot Air Balloon, California Dreamin, and San Diego Balloon Rides.
a person who rides elephants is called a mahout
a bicyclist
It depends on where in Canada you are located but here are some sites for hot air balloon rides. www.sundanceballoons.com, www.blastvalve.com, and even www.hotairballooning.com/balloon-rides/balloon-rides-17.php.
One can find and book hot air balloon rides in Niagara on the 'Balloon Over Letchworth' website. One can also find such balloon rides listed on 'Trip Advisor'.
a buffalo rider
A jockey - or driver.
The equestrian
Jockey
Toruk Makto
It looks like there will be hot air balloon rides at the Spring Poppy Festival!