From Exeter northwards to Collumpton and beyond it doesn't exist, but the B3181 road which used to be the pre M5 A38 is good quality and I've ridden it several times with no problem.
North from there to Taunton I go through Wellington, not round the A38 bypass, and then avoid the Wellington to Taunton section. I prefer using the unclassified roads via Bradford on Tone, they're just more pleasant on the bike.
North of Taunton I've not had any problems. If you want to dodge hills on the northern part of your route you can take the A370 just after passing Brent Knoll and go through Weston-s-Mare, then use the A370 to Bristol. I used to regularly do the W-s-M to Bristol via A370 route, but avoided the Long Ashton bypass stretch, riding through Long Ashton is much more pleasant.
At some point though if you're going to Clifton you have to climb.