
However, personally I'd head either north or west. Dig a map out and join these places up with as many bridleways as you can (and there's plenty of them in those directions):
North: Aldbury - Westland Farm - Pitstone Hill - Pitstone - Ivinghoe - Ivinghoe Aston - Totternhoe - Dunstable Downs - Totternhoe - Stanbridge - Clipstone - Heath & Reach - Rushmere Park - Great Brickhill - Woburn Woods (bivvy). Woburn Woods - Great Brickhill - Stoke Hammond - Soulbury - Wing - Crafton - Cheddington - Horton Wharf - Ivinghoe Aston - Ivinghoe - Aldbury.
West: Aldbury - Cow Roast - Wigginton - Hastoe - Hale Wood - Wendover - Smalldene Farm - Dunsmoor - Buckmore End - Longdown Farm - Princes Risboro - Hemley Hill - Crownfield - Routs Green - Town End - Crowell Hill - Aston Wood - Watlington Hill - How Hill - Cookley Green - Greenfield Wood (bivvy). Then there's loads of bridleways parallel to that route for the return.
Just some ideas
