In reply to Tony Lourens:
There is no direct ferry between Scottish mainland and Hoy. You’ll need to get from Scottish mainland to Orkney mainland then get another ferry to Hoy.
Your option are
a) Northlink from Aberdeen - Kirkwall (6 hours, expensive if taking your car, only calls in at Kirkwall 3 or 4 times a week)
b) Northlink Scrabster - Stromness (90 mins, 3 sailings a day, pretty reliable)
c) Gills Bay to St Margaret’s Hope (about 1 hour 20. Cheapest option but has had some reliability issues)
Then to get to Hoy using Orkney Ferries
a) foot passenger ferry from Stromness to Moaness then either walk through the glen or get Mr Clark’s minibus
b) car ferry from Houton - Lyness but you need to get your car booked well in advance esp if getting a morning ferry H-L and a late afternoon return, these book up about a week in advance but you can usually get over at some point if you are flexible with travel times
c) new foot passenger service starting from Stromness to Lyness from next week. Not so handy for getting to Old Man though.
You can take a bike free of charge on Orkney Ferries foot passenger ferries.