The dales are the opposite direction from York to Bath - not something to do on the way. A separate day trip - fine.
I would do the journey by train - you can relax and enjoy the countryside (and towns) and let someone else do the work.
No idea how long the train journey is, but the 'no-motorway' option on the AA route planner gives 6 hours as the 'scenic' route if you choose to drive.....
Using the train would also ease the problem of parking in Bath.
Journey time by train is between 4 and 4-1/2hrs and is similar for both routes (cross country route via Birmingham or via London). The cross country route is recommended as it's a lot easier to change train in Bristol than have to change stations in London. Timetable and booking (it's normally much cheaper to book some weeks in advance): http://www.crosscountrytrains.co.uk/
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