...which would take around 90 mins from Donny
A bus to Sheffield is part of the airport's masterplan and will presumably be on the cards if growth continues. Direct buses from Sheffield serve all corners of S Yorks, but still not the airport (though strangely there is a direct bus to DSA from Barnsley).
If a nonstop bus isn't seen as viable, a bus from Sheffield via the Parkway / A 631 / M18 stopping at Whiston, Wickersley and Rossington would also serve the local population and still only take around 45 mins. If it weren't for the massive savings that local authorities have been forced to make, I'm sure a bus service would have already been introduced.
Currently the options are a 40 pound taxi ride or a 25 minute bus journey to Doncaster followed by a 25 minute (at best) train journey to Sheffield. Way over an hour with connection times factored in. At the very least, through tickets should be sold at the airport and clear directions should be given.
Hopefully a better public transport connection to Sheffield will be high on DSA's agenda