I actually considered ways to do this when I was younger, but never made it happen. A long fishing rod could be difficult to handle/transport on a bike, even broken down, but it might also be something you could learn to deal with. It'd certainly be easy enough to strap a broken-down rod to the bike's top tube. There are plenty of possibilities there, depending on the type of fishing you're looking to do and the terrain you're cycling on. I can see a portable rod of some kind being great, and the rest of the equipment is fairly light and compact. I'd love to hear about it if you end up putting a trip together.
Who knows..you may inspire me to pull my gear out of exile and get a fishing license next year. I haven't wet a line in...umm...yea. Been a while