The closest stations are Settle and Giggleswick. Both are about 3 miles from Rathmell. Taxis are few, and usually need to be arranged well in advance.
Rathmell is served by the number 11 bus which runs between Tosside, Wigglesworth, Rathmell, Giggleswick and Settle (and then Langcliffe, Stainforth and Horton in Ribblesdale). At the time of writing (Oct 2019) there are two buses a day in each direction (see timetable PDF). For more information on this service and onward bus routes, as well as up-to-date timetables, please visit dalesbus.org
From Kirkby Lonsdale (Kendal, the Lakes, Cumbria and beyond) proceed south-east along the A65 for 17 miles. When signs indicate Settle to your left, look out for Rathmell signposted to the right. This is an unclassified road (commonly known as Rathmell Bottoms… liable to flooding in the monsoon season); proceed along it for approximately 1.5 miles until you reach Rathmell village after the first slight hill.
From Skipton (Keighley, Bradford, Leeds, Harrogate and beyond) proceed along the A65 for approximately 9 miles. In Long Preston, take the small, sharp left turn on to the B6478 (Station Rd), and stay on it for 2.0 miles to Wigglesworth. Turn sharp right before the Plough Inn at Wigglesworth and continue on for approximately 2 miles to Rathmell.
From Clitheroe (Preston, the M6 and beyond), follow the A59 towards Skipton, but turn left and leave the A59 at Sawley. Follow signs to Settle, then Wigglesworth. At the Plough Inn in Wigglesworth, take the left turn and join the throngs making their way to Rathmell from Skipton.