There is no bus service into Ferry Meadows Country Park itself, but it is only a few minutes walk from bus stops in Orton Wistow or on Oundle Road as follows:
OPTION 1: use Stagecoach route 1 to Orton Wistow (Ferryview), which is the first stop in Orton Wistow. Cross the road and continue in the same direction as the bus. Just past the next road junction (Ferryview) there is a path through the trees. Follow this and bear right where the path splits. This will bring you out onto Ham Lane just before the level crossing at Ferry Meadows station (Nene Valley Railway). Cross the railway to reach the country park. To return to Peterborough retrace your steps and catch the bus on the same side of the road where you got off (buses follow a one-way loop around Orton Wistow).
OPTION 2: use any bus on the Orton Mere page and continue two stops beyond Orton Mere to alight at Cherry Orton Road just before Notcutts. Cross the road and walk along Ham Lane from the roundabout to reach Ferry Meadows. Retrace your steps to return to Peterborough (from the stop on the Notcutts side of the road); use the Orton Mere page for timings: buses depart a couple of minutes earlier than shown for Orton Mere.
NOTE: Option 1 is a longer bus ride but much more frequent than option 2, and is also a little closer to Ferry Meadows than option 2. You could always go out one way and return the other for variety.