Hi Frank
You'd probably be better getting the number 31 bus from the main bus station in Warrington (its pretty close to both rail stations).
It should drop you off at the Red Lion but I'm not sure how close it is to walk from the Red Lion to the reserve. It will be at lot closer than walking from the rail station as it is over 4 miles.
The bus eaves Warrington every 2 hours on a Sunday and I think the last return bus is about 7pm.
You can get the full details here:-
Transport Direct - Britain's free online journey planner
Let me know if you need more info.
Alan