In reply to Phil1919:
The DB planner at bahn.hafas.de has an option to select only bike-friendly journeys - if you do it suggests you take the IC-Berlin (total cost around EUR16 on top of your ticket - EUR12 for bike ticket, EUR4 for reservation) and change at Rheine. Bikes, other than encased folding bikes, aren't allowed on ICEs.
Might be worth you giving one of the agencies e.g. Ffestiniog Travel or Rail Canterbury a call, for a few quid they can probably sort it all out for you.
Post edited at 23:51