I grew up in North Devon and spent a lot of time cycling that stretch. Bideford to Barnstaple is a lovely stretch along the bed of the old railway. It's all very fine gravel and there's some lovely views over the bay. Barnstaple to Braunton also uses the old railway line and is again flat and enjoyable.
From Braunton onwards is where it gets interesting, the route leaves the old railway track and looking at their official website, they recommend following the coast. Hilly is one way to describe it, there are some real leg stretchers along that part and the road is narrow with large hedges. It is beautiful and I rode it a lot when I was younger, but it is tough going in parts.
https://www.tarkatrail.org.uk/the-tarka-trail/
@ColinJ has suggested an alternative which is the A361, a less hilly, but busy A road. Not a huge barrel of laughs to ride on.
@Dirk rides these roads a lot I think and would be a good bet to offer more up to date advice for that stretch.
Edit: as pointed out below, I'm a dolt and didn't look close enough

the 361 is not a great road, but Colin's post also didn't recommend it!