I want to ride my bike from Ijmuiden to Schiphol railway station and take it on the train to Groningen - any problem with this?
You can take your bike on Dutch trains. Folding bikes that don't take more space than a normal piece of luggage travel for free, but they must be fully folded during the trip. However, for normal sized bikes you need to buy a bicycle day ticket ("dagkaart fiets") which costs 6,- and can be bought from the ticket vending machines. You will of course also need a ticket for yourself. You need to load the bike in the special bicycle section of the train (marked by bicycle decals on the outside) and you are not permitted to take your bike with you during rush hour. (7:30 - 9:00 and 16:30 - 18:00).
BTW, if you want to get from IJmuiden to Groningen, why not board the train in Haarlem?