In 1958 your easiest option would be:
Gerrards Cross d 11.54
High Wycombe a 12.12
.................... d 12.55
Nottingham Vic a 15.13
Otherwise (see Timetableworld) the local service looks rather fragmented, so you might have to change at High Wycombe, Princes Risborough and Aylesbury, in which case you might as well go via Marylebone.
From High Wycombe this is the 12.15pm Marylebone-Manchester, a train that finished in January 1959. After that passenger services over the Grendon Underwood-Ashendon link were sufficiently few and far between to qualify for the first ever PSUL list in 1963.
After 1958 I looked at moves via Banbury, but it was surprisingly difficult to get from Gerrards Cross to Banbury in those days, despite the hourly service from Paddington to Birmingham and beyond. Few of these seemed to stop at more than one of High Wycombe, Bicester North or Banbury. One move that I found in 1963, providing you don't mind a late arrival was:
6.46pm Gerrards Cross to Bicester North arrive 7.42 pm (6.19 pm from Marylebone)
8.12 pm Bicester North to Banbury arr 8.28 pm (7.10 pm Paddington-Shrewsbury)
9.16 pm Banbury to Nottingham Vic arr 11.35 pm (7.15 pm Swindon-Sheffield)
There was no remotely decent connection from Gerrards Cross to Banbury for the 10.50 am Bournemouth-Newcastle.