This a new page (Jan 2019) collecting info about taking your bike on the bus in the Sheffield area.
Most buses and Supertram in the Sheffield area do not take non-folding bikes (Folders are generally welcome)
Hulley’s of Baslow however do take bikes. We recommend contacting them to check on your particular journey:- T: 01246 582246 E: firstname.lastname@example.org Tw: @hulleysofbaslow
In this respect we are way behind the USA.
Informal (but very useful) bike carriage on buses notably the X70? (connexxions?) Wetherby-Harrogate and around Tadcaster
(possibly 843 Leeds-Malton Coastliner).
1) Trent Barton’s Red Arrow (Nottingham-Derby-Chesterfield coach services) were carrying bikes with bike securing racks in the hold.
3) X70 is the only service I’ve heard regular reports of informal carriage – Coastliner would be very useful though. Elsewhere the 599 (every 20 min in summer) open top service along A591 by Windermere carries bikes on lower deck, & Scottish Citylink is preparing to deliver some useful changes for cyclists with their new app & booking systems – especially useful are the 976 Glasgow-Oban (when the 08.21 train is fully booked catch 08.30 coach) the 915 (Glasgow-Uig) and the 961 (Ullapool-Inverness) basically avoiding some big hills & less pleasant roads from key ferry crossings.
5) A real bargain is the Peak Wayfarer unlimited rail & bus (& tram?) across a swathe from Wigan to Grindleford, the only snag being that the train you get from Sheffield has to stop at Grindleford to use a Sheffield-Grindleford ticket to bridge the gap.