No bus but call Canyon transportation. They run shuttles up there...and I dont think it is more than 20 or 30 dollars. But as far as I know there is no public UTA bus that does that route.
if you can get yourself to the opening of the canyon in sandy, they run buses all the time through there for like, $3 a head or something ridiculous like that.
Hey just hop on the UTAbus, they have sick routes that take you in the mouth of the canyon and then a transfer takes you right up. It might take a little time from the airport though.
