Lots of good info already-

I wear a Camelback hydration pack which has plenty of room for tackle, bike specific tools, spare tube, mini pump. Rod gets bungeed to the side of the Camelback. Sandals for wading get bungeed to the outside of the pack as well. Bike shoes go where the sandals used to be when I'm fishing. It's all about fun - if it's too cold to wet wade in my sandals and bike shorts, it's too cold to take the bike fishing.

For short trips I have often secured a fully rigged two-piece rod to the top tube of my bike with small bungees. Risky, but no problems. A four piece (or more) rod in a tube secured to my pack is much safer, but takes all that much longer to rig up when I get where I'm going.

I can't imagine it is enjoyable in any way to wear waders on a bike. As a kid growing up, I'd wear hip boots on my bike all the time, but good fishing was never more than a couple miles from home.

Yes, I get funny looks from the uninformed, ignorant people who have no understanding of the functional purpose of good bike shorts.