RE: Shortest north east routes.
Washington: when the 83 was renumbered to the 82A in (I think) February 2015, the part of the route that ran from Concord to Heworth was axed. For a while GNE ran a service from Concord to Stephenson Industrial Estate and back to Concord as service number 982 on early mornings and late afternoons to compensate for the loss of that part of the route. The journey was 5 minutes from Concord to Stephenson. I'm not sure if this would count as it only ran Monday to Friday, it consisted of only 7 runs and was effectively a workers special. The service was scrapped after about a year as it was little used.