Fabric velcro strips sewn to elastic strap sections, break the rod down and put it into a tube, use the elastic/velcro straps to secure the tube to the bike someplace. If you really want to strap on a 1-piece rod then sew up a long sock for it lest you find yourself snagging branches and twigs with the exposed line between the rod guides.
A 3 to 5-piece rod can be strapped to the handlebars sideways leaving the rear rack for vest or lunch or net or float-tube.
I really hope to get back into fly fishing this year again, the last few years have been hectic with job searching and family stuff so any fishing took a backseat to everything else.
I think there's a thread on the site here, might be in a different section, with a lot of fly fishing and other fishing photos with bikes in the images. (Might have been a bicycle thread on a fly fishing site, or a fly-fishing/bicycling thread on a photo site, but somewhere there is a thread combining fishing and bicycling, someplace....)
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