-
Scotrail let you book a bike on the website too. However, you can't use the Scotrail (or any other) website to book a bike on the train if the operator doesn't let you book bikes through a website. E.g. I can book a bike spot on a Scotrail train through the Virgin Trains (or any other) page, but I can't book a bike spot on a Virgin train using the Scotrail website, because Virgin don't let you book bike spots online.
So the long and short of it is that if you can't do it on the website you have to call up or book it in one of the ticket offices before you depart (depends how often you're at train stations I guess)
I've got a feeling someone has mentioned Trans Pennine Express or Northern Rail as letting you book a bike.
Also, you can consider going from Kings Cross to Doncaster (Virgin?), and changing there for Sheffield.