Your local independent bike shop will probably be happy to let you have a spare cardboard bike box. Getting a bike to fit in one and protecting the gears and cables is tricky though so it might be worth paying the bike shop to do it.
We use a "next day" courier service but book collections at least a week in advance of the start of your trip for your (and our) peace of mind. Bikes are shipped to our workshop in Inverness where we will re-assemble your bike and check that it is undamaged and safe to ride prior to your arrival. Bikes will usually travel with you from Inverness to John O'Groats. This service is only available if you also book transport for cyclists from Inverness to John O'Groats.
The rate for shipping a standard bike from any UK mainland address to our base in Inverness, including re-assembly is £95. (In addition to passenger transport service.)