This is the family-friendly route through the Two Tunnels to the south of Bath (one is a mile along), then heading back into Bath along the canal, before heading back to the car at Linear Park.
1 - you don't need to go through Bath. We took some advice from a local and I'm certain that you can stay on the canal until it rejoins the Avon.
2 - I've had to rotate the video by 90 degrees, as my Contour wasn't set up correctly… I blame the kids :-)
It's a terrific route, either on traffic-free or traffic-light paths and roads throughout. Note - you don't need a mountain bike, although a racer would get pretty muddy in places.
I make it 23 tunnels and 14 bridges.
We also thoroughly recommend the cafe at the Avon Canal Centre. See more at mombee.com/2013/bath-tunnels-family-ride/