There is no peak hour restriction for international bike tickets, so you shouldn't have any problem.

I would try to travel before 16.00 hrs or after 19.00 hrs between Utrecht and Rotterdam. The trains can be very busy and it won't be easy to get your bike on the train.

I just realised that @Simon Oldfield won’t be travelling on the ICE International between Duisburg and Utrecht because you can’t take a bike on the ICE. So it’s either via Oberhausen, Arnhem and Utrecht or via Duisburg, Viersen, Venlo and Eindhoven.

My recommendation stands to avoid travelling during rush hours in the Netherlands, especially if have to change trains a couple of times.