May is usually ok for riding. Mendips has a rightfully earned reputation for awful mud, so be aware. Gravel bikes will, generally speaking be under-gunned for ‘true off-road’™, but ideal for the many broken roads present around the main plateau. However, the locals use them like luge runs, so it might not be too pleasant an experience.
Lots of good, woodsy, semi-technical singletrack, mostly away from the RoW network. Rocky like the light peak, but not so high. Depending where you’re from, the climbing can be a bit stiff. Fantastic views over the levels from the top of Cheddar Gorge, Deer leap or Ebbor Gorge.
Loads of quaint villages. Pubs can be a lottery. The Swan at Rowberrow and the Plume of Feathers at Rickford, the Langford Inn at, err, Langford, and the Ring o’Bells at Compton Martin deserve special mention.
Chew Valley and the lake is nice with walks all the way around, its been a long time since I went to Wookie Hole with the kids, but we laughed our asses off whilst we were there (15 years ago) in the amusements. Burrington Combe gives reasonable parking and access from the top to Blackdown and Burrington commons (the Ham) for walking/riding.