This is a clear case of confirmation bias.
Any statistically random dataset split down to a fine enough granularity will demonstrate local clusters - just as you may throw three sixes in a row on an unwieghted dice. You are talking about the proportion of cycle commuters in a single postcode so those red blobs could would actually represent a handful of cyclists on a particular street. There are a few clusters scattered around Bath and one of them happens to be fairly close to a cycle path - you need rather more than that to see a causative effect. As others have pointed out - even if that cluster on the A4 is a genuine (if rather small) prefered cycling location it is just as easily explained by the hills.
However, that display of census data really is a powerful visulisation tool that would demonstrate any link between cycle paths and cycle use. If there was any relationship at all then the routes of cycle paths would show up as bands of orange and red on the map - even with the random noise. So to start take a look at the other end of the Bristol-Bath railway path and look at the map of Bristol that others have mentionned - no sign of it. If anything the northeastern sector of Bristol sees lower levels of cycle commuting than other areas.
Now lets look at Warrington, where I live:
http://datashine.org.uk/#zoom=13&la...TTT&table=QS701EW&col=QS701EW0010&ramp=YlOrRd
Now Warrington has a traditionally built central core with a radius of about 2km round the town centre. Normal street layout and a horrible dual carriageway ring road, but nothing in the way of segregated cycle paths. Outside this there are large areas of new-town development (you can see this by the wiggly culs-de-sac and distributor roads) These areas have a network of cycle paths threading through them - yet see the lowest levels of cycle commuting in the town. We also have the national cycle network running east-west through the southern parts of the town - no evidence of that attracting cycle commuters either.
Another example:
http://datashine.org.uk/#zoom=13&la...TTT&table=QS701EW&col=QS701EW0010&ramp=YlOrRd
Eric Claxton (a true believer in segregation) designed Stevenage from scratch around a comprehensive network of cycleways (and set the pattern for pretty much all new development over the past half centuary). Not much red on that map.
Nor here:
http://datashine.org.uk/#zoom=12&la...TTT&table=QS701EW&col=QS701EW0010&ramp=YlOrRd
The mother of all cycle networks where pretty much the entire population has access to cycleways.
Another example:
http://datashine.org.uk/#zoom=12&la...TTT&table=QS701EW&col=QS701EW0010&ramp=YlOrRd
Compare and contrast Shrewsbury with a compact tradititional street network - to Telford with its network of cycleways.
I could go on, but wherever you look on the map, those towns with the greatest concentration of cycleways see low levels of cycling.