I used to book about 20 coaches every summer, leaving Sheffield to go to various destinations. (I was organising inter-regional youth cricket teams). One year I wrote to over 50 companies in the area, seeking quotations for our needs. It quickly became apparent that the prices charged by Sheffield coach firms were generally far higher than those charged by similar companies based in Rotherham and Barnsley. (Sheffield firms generally charged at least 50% more than firms from outside the city. In many cases the Sheffield companies were seeking more than double what their rivals from down the road wanted).
The only way you'll get definite figures is by phoning around (or writing to) a few companies but I strongly advise you to contact firms in Rotherham and Barnsley, as well as those in Sheffield.
The firm which gave the lowest quote of all (by a significant margin) provided consistently excellent service. While that was quite a few years ago, I think it's likely that they'll still be both cheap and reliable. So here's my recommendation for you:
http://globecoaches.com/
Chris