IIRC both of those lines are run by companies that don’t let you book a bike on in advance, so it’s first come, first served. That said all trains have space for at least two bikes so you’re good if only one other person turns up. If more than two bikes it’s down to the train manager’s discretion, be polite about it, make an effort to keep out the way and you should be fine.
As regards being muddy, get any loose stuff off and don’t sit down, no problem.