There are several pleasant routes into Bath avoiding the city
traffic:
From the west:
The Bristol and Bath Railway Path forms part of the "Sustrans"
route 4. The path is 19kms long and level nearly throughout,
offering a very pleasant path for cycling or walking between the
two cities.
http://www.sustrans.org.uk/
From the north:
You can avoid the traffic by joining the Kennet and Avon Canal
at Bathampton and then coming into the city along Great Pulteney
Street.
From the east and south:
The Colliers Way is a 23-mile long multi-user path between Frome
and Bath via Midsomer Norton and Radstock. It is part of National
Route 24 of the National Cycle Network. It joins Sustrans Route 4
at Monkton Combe and the route runs alongside the Kennet and Avon
Canal for the final 6kms into the city.
www.bathnes.gov.uk/colliersway
Many people enjoy cycling along the Kennet and
Avon Canal towpath.