There are no major direct shuttle services between Scottsdale and Prescott, Arizona. It is possible to make this journey with a stop at Phoenix Sky Harbor International Airport, which is a hub for shuttles between the two destinations.
RoadRunner is a service that can connect you from Scottsdale to the airport. The fare for this leg is $18 per passenger, according to RoadRunner's currently published fares as of July 2015. You can transfer to Arizona Shuttle, which will take you from the airport to Prescott for $35, according to Arizona Shuttle's fares as of July 2015.
To get to the airport for under $10, you can use Valley Metro service. It involves more stops and a longer travel time. Take the Route 81 bus southbound on Hayden to McDowell Road. Then take a westbound Route 17 bus to 44th St, walk or wait for a Route 44 bus to take you to Phoenix Sky Harbor Airport, and then take the Arizona Shuttle to Prescott.