We recently took two bikes from Chester to Holyhead and back again when we toured Ireland.
From Chester to Holyhead it was a piece of cake. We managed to phone Aviva and make sure that the bikes were booked on the train. We had a reference number. The lady on the station at Chester was amazing, tidying up all the suitcases that were strewn everywhere in the bike section and helping us hang the bikes. On this particular train there were 4 hooks to take 4 bikes hanging from their front wheels.
Be warned though, when we booked online there was nowhere to book the bikes. When we asked at the local train station they had no way of booking them and advised us to just turn up. They even phoned Aviva and they said to just turn up. However I phoned the call centre myself and spoke to a very helpful chap who I assumed was in a far flung asian call centre, but he managed to book us on. It was a relief to know we were definitely going to get them on.
The return wasn't as easy. We hadn't booked this train, and the layout of the carriage was different. Instead of the hanging hooks, there was just a space to strap them inside the main carriage. Everyone then piled up their luggage around them, and getting off at Chester with them was a complete nightmare as there were hoardes of people trying to get off behind us and on in front of us, while we tried to get bikes, panniers, tents and sleeping bags out. There was another bike on at the same time, but it was a folding one. I'd definitely try to book just for peace of mind.
If you're not getting off at the end of the line it may be a stressful experience.