Was there any reason behind the 44N numbering? Seems rather random given the 44 (which Scotland East operated at the time) was a completely unrelated route.
Going back a generation, the 42, 43 and 44 were bus numbers between Edinburgh and Bo'ness via the A90 & South Queensferry so probably something to do with that. Not sure exactly when the 44N started but have a recollection of something like this operating at weekends in the mid-1980s, probably using the A90 route but I don't know for sure as I think it later used the A8 (similar to the 38). I don't think the 44 between Balerno and East Lothian was around at that time. The old 52 to Balerno was replaced by 64, 65 and 66 numbers when the route extended to Penicuik, then eventually the Balerno routes copied LRT's 44, which is when SMT or Grampian introduced a day service with the same route number.
Anyway I believe there was a time when this 44N from First and the N44 from Lothian both ran along Princes Street and Shandwick Place, which may have led to surprises amongst those who had over-indulged during the evening.
I think this went around 2012 the 44N went but new night service Edinburgh - South Queensferry - Kirkliston - Linlithgow, can anyone remember that?
Yes, if I remember rightly that was the 43N (or perhaps N43). The route was a bit unusual because from Barnton it went straight out the A90 to Echline then made a clockwise loop around South Queensferry before heading out to Kirkliston, Winchburgh etc to Linlithgow.