Snyman replaces Andries Strauss who was suspended for two weeks for his dangerous tackle on lock Wikus van Heerden in the Cheetahs' season opener against the Lions in Johannesburg last week.
Drotske, who announced his team on Wednesday for the weekend's clash, also included youngster Willie le Roux at wing for the injured Dusty Noble.
Noble injured his knee against the Lions and will be out of action for at least eight months.
Le Roux, who earns his first start of the competition, is playing in a somewhat unfamiliar position - he normally plays at flyhalf or fullback - but he was eager to get his first start in Super Rugby.
"It is something that I have worked towards my whole career, earning that first start at Super Rugby level," Le Roux said.
"It is the first time I will be starting a game as a winger, but I am still looking forward to getting my shot.
"I've switched to wing before during a game, but never started as one."
Fellow wing Cameron Jacobs, recovering from a hip injury he picked up in a Varsity Cup match for Shimlas, will start on the bench.
Le Roux, who came on as a replacement against the Lions, said he would put in the hard yards as the hosts aimed for their first win of the competition.
"The game against the Lions is a thing of the past and we as a team are now looking forward to taking on the Bulls on our home ground," he said.
"I am also hoping to deliver on my individual performance.
"I won't just be standing around, but will be looking for work all over the field."
Teams:Cheetahs: 15 Hennie Daniller, 14 Rocco Jansen, 13 Robert Ebersohn, 12 Philip Snyman, 11 Willie le Roux, 10 Johan Goosen, 9 Tewis de Bruyn, 8 Davon Raubenheimer, 7 Philip van der Walt, 6 Heinrich Brussow, 5 Izak van der Westhuizen, 4 Andries Ferreira, 3 WP Nel, 2 Adriaan Strauss (captain), 1 Trevor Nyakane.
Substitutes: 16 Hercu Liebenberg, 17 Lourens Adriaanse, 18 Waltie Vermeulen, 19 Ashley Johnson, 20 Piet van Zyl, 21 Sias Ebersohn, 22 Cameron Jacobs.
Bulls: 15 Zane Kirchner, 14 Akona Ndungane, 13 Wynand Olivier, 12 Francois Venter, 11 Bjorn Basson, 10 Morné Steyn, 9 Francois Hougaard, 8 Pierre Spies (captain), 7 Jacques Potgieter, 6 Deon Stegmann, 5 Juandré Kruger, 4 Flip van der Merwe, 3 Werner Kruger, 2 Chiliboy Ralepelle, 1 Dean Greyling.
Substitutes: 16 Willie Wepener, 17 Frik Kirsten, 18 Wilhelm Steenkamp, 19 CJ Stander, 20 Jano Vermaak, 21 Louis Fouché, 22 JJ Engelbrecht.