Around 2 miles in a straight line, but some of those options are so indirect as to end up almost as long as using the former branch line Phoenix Trail to get to/from Princes Risborough instead. No, I'm not suggesting that as another alternative; there are already far too many options offered, and this whole thing does seem in danger of frittering away a large budget on feasibility studies and consultations without actually resulting in anything happening on the ground.

Ultimately for this to be a facility people use on a day-to-day basis rather than just for a leisure trip on a sunny afternoon, it has to take something close to the most direct route, rather than winding around paths through fields just because they are simpler to upgrade and avoid having to do anything about motor vehicles. Alongside a road is also far less isolated after dark in particular.

 
Very cyclable distance. Terrible infrastructure on which to cycle. Plans afoot and here's a consultation.

https://letstalk.oxfordshire.gov.uk/h-to-t-active-travel-route