[QUOTE 2429816, member: 45"]Ooooh thanks. Are they ok with you just catching the bus one-way? (I've had problems before with awkward drivers)[/quote]
I'm fairly sure it's fine, and those buses act as service buses along the way. The park and ride you want is Rawcliffe Bar
http://www.itravelyork.info/park-and-ride/park-and-ride-sites/rawcliffe-bar/
Looking at fares, they say that journeys starting in the city are at normal service rates, so yes it should be fine.
http://www.itravelyork.info/park-and-ride/fares-and-passes/
You won't have a bike with you I guess? The riverside path goes north and passes the back of the Park and Ride site. It would be a long walk, though quite a nice one. 3 miles or so. Go down to the river from the NRM, via a little alley, cross the footbridge, turn left and follow the river north.
(Unless it's flooded. Being May, it might not be, but it's always a possibility!)