I enjoy cycling and prefer to use my bike to go fishing, especially as my favourite marks are within five miles of my home. It's possible to carry a normal beachcaster strapped to the top bar but I use a Penn Seatrek and Penn Jetstream which are three and four-piece rods. Multi-section rods nowadays are just as good as two-sectioned ones and are a lot safer and easier to transport this way. The Penn Powerstick has had good reviews on this site and is available for around £40. Imax have just released a range of excellent three and four-sectioned rods, to name but one other company producing multi-sectioned rods. If I fish a beach then I use a telesopic tripod. A good quality headlamp eliminates the need for a petrol lamp.
The rest of my gear I carry in a Titan Matchman's rucksack. If you can't get all your tackle into one of these then you're probably taking too much. I find it comfortable enough for moderate distances but you need to take things easy as rucksacks raise the centre of balance. If you're riding at night then you need to either buy a brightly coloured one or fix reflective strips to it. It's not advisable to carry anything dangling from the handlebars for safety reasons. :uhuh: The catch, if it's a large one, can be carried on a rear rack. Alternatively, and especially if you have to ride on busy roads or have much distance to travel, you could think about using rear panniers to carry everything, which would be the safest and most comfortable way.
If feel you must go fishing with a quiver full of rods and use a beach shelter then you need to take your car. But using a bike forces you to take - and buy

- only what you really need.
Cheers,
John