Hmm unless you mount a one piece pole like a cb antenna and go slow I would think it's like expectancy would be short. Most poles would be longer then the bike, so mounting horizontally is out of the question. You just don't like two and 3 piece poles or do you fly fish?
I am a fly fisherman. Have not gone fishing on the TW much. But when I do I have a very nice travel fly rod that packs into a tube of just under 20", so it fits easily in a backpack. That along with a fanny pack size fishing pack which holds everything else including the reel is all the equipment I need to fish. Many companies make nice travel rods now, all but the worst cast just as well as the 2 and 3 piece models. The one I have is from Orvis, if I remember right it cost about $200.
Rich, thanks for the Sunday morning laugh. Hadn't seen those Bill Dance bloopers in a long time. The snake falling out of the tree is classic!
Jake, I fish mostly for trout in the Eastern Sierra and use light-weight gear. The rods I use are two pieces that I stuff in a backpack. Less than 15" sticks out of the top of the backpack. Works well for me.