You can arrange it in advance, many cargo ships carry limited number of passangers. There's a Finnish writer who has done quite a few long haul tours on cargo ships since, dunno, about 1960s. She has also published several logbooks of her travels. From what I gather you need to be flexible with schedules, your ship's arrival to destination may be days off from what it says in the brochure. Also, cargo companies vary their routes according to what needs to be transported, so you may have to change ships in some port. The ships may take long time loading / unloading cargo, so complimentary stops are there. You just need to arrange for local transportation, cargo ports are seldom in city centers, or within the reach of local public transportation even.
In general, the author of the logbooks seemed quite satisfied with the service. It's not cheap though. Your local travel agency might have some pointers as to where to look. I've been thinking about such a trip too. I would imagine carrying lots of gear (including bike) would not be a big problem, it being a cargo ship and all.
--J