Given the times and destinations of the flights to and from DSA I agree that a fast non-stop bus service to Sheffield wouldn't be viable. Any new bus service would need to serve the local S Yorks community as well as the airport.
I'd argue that South Yorkshire Passenger Transport Executive (SYPTE) should introduce a fast stopping service that serves DSA and the business park, Rossington Village, and the west Rotherham suburbs of Wickersley and Whiston, using the Bawtrey Rd dual carriageway instead of the M1 before traveling down the Parkway into Sheffield.
With the new link road in place, even this route wouldn't take more than 45 minutes which is acceptable for an airport to city connection. It would be used by local passengers too as a quick route into Sheffield and connections beyond.