I'd echo what User10571 said above re the Crab & Winkle Way. However, allow at least 45-50 minutes to get from the Waterfront to Canterbury Station. Some new bits have been tarmaced in the last year or so, but at least half is still gravelly bits.
For then getting to Ashford, you can either do hills or the A28, or a combination unfortunately. The least worst option would be to head out of Canterbury, and then after crossing the A2, turn left to join Cockering Road for a few miles to then re-join the A28 by Chilham station for a mile or so, and then turn off left just before Godmersham, join Sustrans Route 18 and drop down through Wye, and then there's a shared use bridge over the M20 to then follow the A292 into the town centre.