It is pretty easy to carry a fishing rod on a bike. Here is my fly rod on my MTB along with U/L camping gear:
You could use pvc pipe if you don't care about weight or the lighter tubes made to slide over flourescent light tubes, but I find a cloth sleeve adequate.
The light tubes I mentioned are these:
Lithonia Lighting 4 ft. Fluorescent Tube Protector-TGT12CL4 R24 at The Home Depot
They are pretty cheap, readily available, and can be cut to length. You will need to make or find an end cap of some sort to fit, maybe a standard pvc cap or a wooden plug?