Public Transport

To go: train to Weston-super-Mare, then bus

To come back: bus to Weston-super-Mare, then train

My preferred solution

Saturday, 7:52 a.m from London Paddington, arrival 11:54 in Cheddar

Sunday, 18:54 from Cheddar, arrival in London Paddington at 00:18.

I'll update with alternative trains.
If some of you want to share the hotel and organise with a car, feel free.