Ideally looking for times it leaves Tedder Road heading in to York. The current timetable doesn’t show me Acomb to York, just the reverse. If I knew they started service at say 0620, I could assume that the next buses would be at 0650 and 0720 etc., preferably allowing me to catch the latter to York for my train at 0830.
From the
top of Tedder Road, it's only a 10 minute walk to Ridgeway for the more direct Number 1. Overall that probably isn't quicker by the time you've done the walk but it's an option to be aware of.
Google suggests there is a bus due from the Askham Lane stop (at the top of Tedder Road) at 0751 which gets to the rail station at 0811; this is consistent with the entry in the link provided above by
@darloscott which shows timing points Foxwood Shops 0754 and Cliffords Tower 0815.
That would give you loads of time for the connection; indeed the bus after that should make it in time for your connction too.
And if there's any issues with the number 4 route, or if you fancy a walk, there appears to be a number 1 bus from Ridgeway at 0805 which arrives into the station at 0818.
(Of course if you're going from the
bottom of Tedder Road, you'd be using the Foxwood Shops or Huntsman's Walk stops)