The location of Leeds Bradford airport has always been problematic, no rail link, not particularly near any motorways, highest airport (according to wiki, but not sure on the definition of 'airport') in England at ~600ft/200m above sea level makes for difficult conditions both at the airport and on surrounding roads in winter. Also because of location subject to crosswinds.
Although the nearest rail line (Leeds Harrogate) is only about 1 1/4 miles away, geography means that a heavy rail link to the airport is impossible without major civil engineering, same thing applies to Apperley Bridge. A bus link from a station to the airport is going to have to negotiate the roads around Pool in Wharfedale and Pool Bank.
If you built a new road link its might connect at a railway station, but then non rail traffic is still going to have to go somewhere, and there are no decent link roads to the M62 axis.
If lots of funding was available one could imagine a tram - train solution, perhaps a loop from Leeds to Horsforth then via the airport to the Ilkley branch, and back to Leeds, but I dont think potential usage would justify costs, and there would still be a lot of civil engineering probably including tunnels.
In the 70s there was a scheme to build a motorway from Dishforth to Pudsey and on to the M1, before the M1 was taken east of Leeds. This would have improved access to the airport and the whole area north and west of Leeds, but it got killed off pretty quickly.
Rail wise there was the link through Otley from the Harrogate line to the Ilkley line, and if this had survived would probably be quite well served today, but this wouldn't have helped with airport access.
If the P&R is built you still have the problem of the capacity of the surrounding road network.
A better spot for a Park and Ride might be between Pannal and Weeton close to the A61/A658 junction, with access of the junction, at least there are decent roads to get traffic out of the P&R area, this could be usefull for both Leeds and Harrogate travellers, and I could even see benefits in stopping the Harrogate - London services there.