Simon, if it helps, I had exactly the same problem booking from Oxfordshire - I resorted to the old human-being interface at the station. (Having checked there were bike spaces on the standalone leg).
Annoying, isn't it?
80:20 rule in action. You can handle 80% of the users of the GNER booking website with 20% of the work implementing the site.
Handling all of the niche requests, i.e. "people who want to book a journey spanning multiple train operators and get a bike reservation for the whole journey, but one of the operators/trains doesn't have bike reservations and so alternatives should be checked and offered etc" takes up the other 80% of the time, for much less return.
Complaining/giving feedback may prod them along to investigate it and improve it. If you/we don't then they're unlikely to ever find out that it's a problem/annoying themselves.
My usual method is:
1) Do a search and see if it's possible to book the whole way in one go with bike reservations, if they are, and the price is reasonable, buy them and be done with it.
2) If not then look at what changes are required (and where, and between which operators) and where the problem lies, then look for alternatives cutting the journey up into appropriate segments based on the changes. This can also work for expensive tickets as you can often find which leg is contributing most to the cost and look at the alternatives.
3) Book/reserve as required, but don't checkout until you've got all journeys covered; that way you don't end up buying tickets for several legs of the journey only to find that the final leg is impossible to book with a bike.
