Become a supporter
I've used most of this route at various times apart from short sections around Bridgwater but I expect they're OK. I think this offers an easier crossing of the Mendips by using the Shute Shelve tunnel (it has some lights but it's easier if you take your bike lights!) and an easier access to Bristol by using the Festival Way. It might be fun to take your bike on the train down to Taunton and ride back to Bristol.
Last time I used the three main rough sections of this route (alongside the canal in Taunton, the Strawberry Line and the Flax Bourton Greenway), all three were OK stonedust and level or gentle gradients. If you want to choose the spectacle of climbing over the Mendips or entering Bristol over the Clifton Suspension Bridge, go for it, but I think this is an easier option and has its own beauty spots.
A fun ride across the fens - much easier if there isn't too much wind. Going through Outwell and Friday Bridge rather than Emneth and Elm avoids some rough roads, but still contains several more-than-a-mile straights (pictured). There are shops at each end and in the bigger villages. There is a pretty good cafe for lunch called Panini's in March Town Hall. Easiest bike parking (pictured) is in the middle of Broad Street, before you reach it.
So the Clapham Road / Union Road roundabout is planned to become a turbo roundabout. Chris Peck of CTC has put up a blog post about this at http://www.ctc.org.uk/blog/chris-peck/cycle-safety-fund-and-bedford-turbo-roundabout-some-facts and there is a note from the scheme designer at
http://bicycledutch.wordpress.com/2013/05/09/a-modern-amsterdam-roundabout/#comment-6142 (from March 2013)
Only CTC members are allowed to comment on Chris Peck's blog, so I'll just note here that I'm horrified that wasting cycle safety money building bad designs was considered preferable to rolling the fund over to a new round or handing it back, despite this supposedly being a time of austerity.
The note from the scheme designer makes clear that bikes came a poor third place. I don't really buy much of his bid: the background PDF linked by Chris Peck seems a bit misleading. Some examples:
I could continue, but I'm surprised it didn't fail hard. I can only dream nightmares of what the less-desirable proposals were.