Short answer is Yes. Northern Rail is the rail company that serves the Yorkshire area, including the Yorkshire Dales National Park bits from Skipton northwards and Dales Bus has all the info on buses (and links for trains too) serving the Dales. See
http://dalesbus.org From the airport Flying Tiger buses will take you into Leeds and Bradford for onward connections, see
http://www.flyingtigerbus.co.uk Lots of places for accommodation but that will, of course, depend on where you wish to visit. Skipton is a large town and has supermarkets, shops, cafes, restaurants and with bus and rail links to virtually all of the Dales 'hotspots'. If you prefer something smaller and quieter, then Settle (I may be biased here) also has a supermarket, shops, cafes and restaurants and is handy for the 3 Peaks and Malham, and Grassington (shop, cafes, restaurants) handy for Warfedale, may be suitable. Lots of smaller towns, villages close to rail and bus links should you want quieter still, but with less facilities.
If you have a plan of where you are going to walk and what you need re accommodation, food etc., that may help in being able to offer more specific advice.