This from Andrew Richardson:
Interesting article in the Yorkshire Post suggesting that the ferry will be carrying bicycles free of charge. I believe that last year, they weren’t allowed to take bikes because The National Trust has forbidden it. Does anyone know any more about this development. Useful if correct!
York Wednesday Wheelers 
This seems to the definitive information on the Nun Monkton ferry and carriage of cycles:
“Weather permitting, the ferryboat will run from Saturday 6th April every Saturday, Sunday and Bank Holiday Monday until the end of October 2019 from 11am – 4pm. A small charge of £2 per adult and £1 per child each way will be made to cover running costs, with dogs and bicycles being transported for free.
“Please note that bicycles are only allowed on the crossing between Nun Monkton and Moor Monkton and cannot disembark at Beningbrough. The above offers a crossing of the River Nidd only.”
My OS maps show a bridleway between Moor Monkton and the ferry landing on that side of the Nidd. On the Beningbrough side of the Ouse there is only a footpath.
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