I bike and I fish but only twice have I biked somewhere to fish. Nonetheless, when I fish I use telescopic rods (that collapse down to less than 2ft) for any fishing that doesn't require my 2-piece 10' and 11' surf rods. Telescopic rods come in various lengths (I like 2.4m and 2.7m for casting distance; I primarily fish saltwater) but are limited to ~3oz casting weight. When collapsed down they fit into a backpack or pannier bag (roll top with the top open), or you can just strap it to a rack.