(This site is Edinburgh biased.)
Sustrans NCN Route 1 follows (roughly) the east coast of England and Scotland and passes through Edinburgh and Fife.
From the centre of Edinburgh to Fife (via the Forth Road Bridge) is about 10 miles. (CycleStreets routes.) It could be better in places and there is a long standing campaign by local cycle group Spokes to get improvements.
A great way to get to Fife is by train. There are frequent trains and several routes through the Kingdom. There are 19 stations – room for plenty more… (Timetables – look for Fife Circle and Aberdeen trains.)
There are several stations just across the Bridge including Dunfermline for the start of the West Fife Way and the Dunfermline Charlestown Limekilns loop.
Kirkaldy is a good place to start to explore the East Neuk which includes Fife’s famous fishing villages. Ladybank, Cupar and Leuchars can be starting points for north and east Fife.
Cycling in Fife 
[…] Fife, just across the Forth, is a great place for cycling for short trips or long ones. It has 19 stations so plenty of scope for starting from Edinburgh, getting off at one station and returning from one […]