Yes you can book on the day at the ferry ports. It's unlikely that with a bike there would ever been too little room. But be warned, some of the ports with infrequent sailings (Le Havre, Roscoff, etc) can be completely dead and deserted between ferry sailings. But eventually someone pitches up a couple of hours before your sailing, and will happily sell you a ticket.
One thing to watch is that the price structure on the ferries seems to be changing. It used to be that last minute, standby type tickets were pretty cheap, but more companies seem to be following the Easyjet and other budget airlines, by never undercutting those who bothered to book early. SpeedFerries have gone this route (although they don't carry bikes) and I have heard heard of another switching to this, but I can't remember which one it is.
The other option on routes with traditional ticket pricing, is to book on the last date you could possible return to give you that guarantee and then, if you're early, just ask to be allowed on the next available sailing. I've always been let on.