Planning an overnighter west of London in a couple of weekends time. Due to commitments on Saturday, we'll grab a train out in early evening, find a bivvy spot and then ride back in to town on the Sunday. Trains west of Reading are replaced by buses, so we're contemplating just going as far as Reading and heading into the Chilterns.

My friend won't be on a mountain bike, so not looking for chunky off-road routes, but I could do with recommendations of rough areas to head for where we might find some nice spots to bivvy for the night...

Are trains running from Reading to Goring?

That's on the Ridgeway, then you could head North East for a bit and get a train back into London from Aylesbury or somewhere else in Buckinghamshire.

I guess it depends how much riding you want to do in that eve. Getting onto the ridgeway is a good shout (if dry), although i find the bivvying options slightly reduced on that side of it. (well just a bit further off the way)
If you hide from early riser dog walkers Aston Rowant nature reserve is an option, and there are nice accessible non private woods in Ipsden and Stoke row.
If you wanted an real easy option I have a farm just outside Henley with a field for wild camping (just water and an outside toilet) which you're welcome to use/share with some sheep