Only a couple of companies do that route. I couldn't say how frequently, but I arrived at Quitumbe and was on a bus to Otovalo 20-30 minutes later.

You really need more time for Quilitoa if you are going to do anything but just look at it on a tour. Stay a few days in Chugchilan, get transport to Quilitoa and walk back, wonderful walk. What we did was to rent a car in Quito, drove to Chugchilan, stayed there 4 nights, then drove to Cotopaxi, stayed in one of the haciendas and walked up to the refugio (the tourist walk as someone described it). This way we avoided the tours and being trapped by the tour at Cotopaxi. We could probably have booked the downhill bicycle ride separately if we had wanted to do it.