We camped at Salcombe Regis Camping and Caravanning and it very good. Excellent showers and constant hot water + electricity for the motorhome was a boon. (Not up to Caravan Club standards but still very good). It was recommended by a Sidmouth resident.
We used the Alpha Bus service which was basically hourly (with a meal/rest gap at lunchtime and evening). Last bus at 1.00 am which to be honest was a bit too early for a night owl like me). Drops off near the Radway/Swan and thus very handy.
Some of the Alpha services in the evening (late evening they are every 30 minutes or so) could be very crowded. But everyone got on and there was often some singing (generally "The Wheels of the Bus.......). The two drivers (husband and wife) were very friendly and the cost was £1.50 in each direction which was reasonable. No season ticket.
Apparently the Cricket Club is now £35.00 a night and I was assured could not be booked. Spaces are on a first-come, first-served basis. There may be a discount for a week. Whilst this is expensive (Five Star Caravan Club site is £20.20) it is very convenient and I would consider it for future years. I took a peek at the showers and they are communal but looked of high quality.
Don't know about the Rugby Club but the showers are rumoured not to be first class!!
A couple of years ago I discovered the Sailing Club showers paying (I think 50p a go. Don't know if that still goes.