Hi McDave,
I have a 4 piece Sage fly rod that breaks down pretty small (probably a 28 inch tube to carry the rod). Instead of a vest I use a little chest pack from Cabelas for my fly box, reel and a few tools. No waders, just river sandals with felt soles from Simms.

I also have a Daiwa spinning rod/reel combo that breaks down into two pieces about as long as my fly rod case. Not sure I'd want to take this rod/reel backpacking or touring because of the bulky reel but it's possible.

On the bike I would just strap the tube on the rack along with my tent's drybag. It would hang off a little but it's so light you'd never notice. I'd be more scared of theft than damage. Those rod tubes are very tough.