The National Trust have opened a bike hire facility at Calke Abbey at very reasonable rates. They have created a series of trails to provide scenic and traffic free routes which are excellent for new cyclists or those returning to cycling.
The trails include the historic Tramway Trail.
There are also occasional organised rides for small groups of people wanting to get back into (or new to) cycling and which can include a loan of a cycle. Likely to be quickly booked up.
Check the opening times for the cycle hire as it isn’t open every day. Note that non National Trust members in cars will probably have to pay a fee to enter the Park.
I can also recommend the Milking Parlour for a refreshment stop (just outside the Park). This is the brewery tap for the Tollgate Brewery and has lots of outside seating and some nice beers.
Well Done to the National Trust for this initiative to encourage more take up of cycling and to allow visitors to visit a lot more of their estate.