Travel in the Cinque Terre is not difficult. It would help to know a bit more about your plans, such as where you'll be travelling from?
There are two rail "gateways" to the C.T. - Genova and La Spezia. There's a small local rail line that runs between the two cities. Depending on which village you choose to stay in, the rail trip can be very short (ie: from La Spezia to Riomaggiore is only about 8 minutes).
I'm not sure it will be possible to bike between the villages? Some of the trails are quite steep. Hiking is the normal activity. One can hike from one end to the other, and then take the train back to their "base" location.
I would recommend staying in just one village. Have a look at Rick's Italy guidebook (or others) to get some idea on the different character of each place. I stayed in Riomaggiore and had a great time! You could also check the C.T. website.
If you need any further info, post another note.