There are four ICEs from Brussels to Cologne each day. If these times suit, it is easiest (and usually quickest - from about 3 hours to Bochum) to book on these (changing in Cologne). These can be booked easily on-line on the DB website.

If I were the OP, I would consider doing it this way - less hassle if you're not familiar with the European train system and you don't want to be changing trains two or more times.

Aviatrix - you're right, the €34 wasn't walk-up. But the €51.60 walk-up fare involves more changes and a significantly longer journey time on less comfortable trains, than taking the ICE.