The town of Worksop is less than 20 miles from Sheffield, yet there are no buses between the two places
Good shout - Dinnington is in South Yorkshire but (the much bigger settlement of) Worksop is over the border in Nottinghamshire so public transport gives up!
One other example around Sheffield is the old UniversEighty (or "80" as old fashioned people would call it), the First SY UniLink service that used branded ex-London double deckers in a horseshoe route linking the Halls Of Residence at Endcliffe to the University Of Sheffield in one direction (terminating on the edge of the City Centre at Mappin Street) and the Hallam University buildings on Ecclesall Road/ City Centre/ Bus Station in the other direction. Every ten minutes both ways, discounted Student fares, late night service etc. This was around ten years ago.
Only problem was that the University were knocking down the Halls around this time (modernising them, replacing 1960s tower blocks with something more like twenty first century), so the service was cut back to an extension of the 44 beyond the Hallamshire Hospital every fifteen minutes (no service to Ecclesall Road), then cut back to a half hourly Stagecoach loop, then eventually an off-peak diversion of the Sheffield Community Transport 10/10a which provides an hourly Optare Solo around the inner city suburbs, such a circuitous route (which runs nowhere near the lecture theatres/ Students Union) that it'd be quicker to walk to the City Centre.
If First had waited until the Halls were re-opened, it could have been a great money spinner, but Endcliffe went from getting a "turn up and go" service (at a time when nobody lived there) to an hourly off-peak Solo (that is more about box ticking than providing a worthwhile service).