• Did the 13 follow the 194 route exactly I.e. Heworth - Concord - Washington - Fatfield - Newbottle - HLS - Easington Lane?
  
• Did it only run Monday to Saturday? (From your recollection?) 
  

(11 Mar 2024, 7:54 pm)Andreos1 wrote The only one I can answer with any certainty.

For a period in the early 90s, they ran an hourly service which competed with the 194. 
If I remember right, it was numbered the 13. It was scheduled to pick up outside Biddick and St Roberts dead on kicking out time. 
Wear Buses as it was at the time, whacked an Optare Metrorider in front of it as a spoiler 194.

I'm sure the shortlived Barnwell to Newcastle 191 was the legacy.