I can't find details of any coaches from your area for the RHCP gig.
Ticketline are only running a coach service from Liverpool and Manchester. Concert Travel are only running a service from Hull, Hessle, Beverley and Huddersfield. National Express have no special concert services scheduled other than for the Take That gig at MK Bowl. (Take That? Are they still around?!!!). Nobody, it seems, thinks that a coach is wanted from Harrogate or Leeds for the RHCP gig..
As long as you can get to and from Leeds, you'll have no problems travelling by rail. There are fast trains from Leeds to Sheffield (with a journey time of just 41 minutes) at 10 minutes past each hour. (There are also slower services to both Meadowhall and Sheffield). The last train from Sheffield to Leeds leaves at 2359.
See my other responses, to your previous question about travel to this gig, for more information.
Chris