This
web page has all the details, not good news I am afraid.
"What about Cycle Reservations?
Space to carry cycles is often limited and advance reservations are compulsory on some services. Passengers should check before travelling. Cycle reservations can be made when booking your ticket(s) on 08457 55 00 33.
Tandems, tricycles, cycle trailers, motorcycles, motor-scooters, mopeds or any other mechanically driven vehicle (except mechanically driven wheelchairs and light travel scooters)
cannot be carried on any ScotRail service. "
This page has some interesting but very brief snippets on carrying bikes on all the different GB train companies, proper details (including info on tandems) don't seen to be available from a single place.
As
Eddiethelaowai says, it may be worth checking other companies, provided they go where you want to go!
Good luck, let us know what you find, it may be useful for others!
T