Watching your canine take flight after the neighborhood kid on the bike can be terrifying. God forbid your dog catches him and potentially causes injury as they pull him off his bike. In fact, even if your dog never touches the kid, he may simply scare him into making a mistake and hurting himself. Even in cases like that you could be found liable and suffer major financial restitution and your canine could be put down. Regardless of their intention, be it to attack or just lick to death, this type of chase is considered aggressive behavior and should be dealt with as soon as possible.
The Root of the Behavior
The root of the behavior comes from an innate sense of the hunt. A speeding bike gives your dog something to chase, something to catch, and that feeling in itself is enough to motivate a canine to take flight. This behavior originates from the predatory instincts of the canine. They are biologically designed to give chase and those instincts have been ingrained into the canine DNA. This just goes to state that it is a perfectly common and natural reaction to a bike flying down the street. The same impulse that causes them to try and chase down a squirrel or a rabbit is what causes the canine to give chase. This is not to say that it cannot be corrected. There are several different steps you can take to reduce or eliminate their actions even though that biological impulse will always remain intact. To your canine, it feels more like a game than anything else. The biker normally would continue to outpace the dog and the dog in-turn continues to chase.
A biker aware and educated on canine behavior would likely stop their bike, turn to the dog and wait it out like a Mexican standoff. This would show the dog that this is not a game and the dog would likely not continue to try and chase someone who is not rushing away from them. None of this is to take into account just your canines general friendliness and social interests. Your dog may not be really taking off after the biker however chasing down someone in which they would like to be friends. Unfortunately for the biker, or at least to the biker, it makes little difference. The sight of a dog coming at you can be a terrifying one even if the dogs intentions are pure. This can lead to accidents or mistakes in judgement on behalf of the biker that could lead to serious injury.
Encouraging the Behavior
This is still considered aggressive behavior even if your canine has no intention of hurting anyone. As such it really should be dealt with as soon as possible. If you are not contacting a trainer yourself, then your first step should really be containment. Make sure your dog does not have the ability to chase anyone down. Keep them fenced or leashed until you are decently sure there will be no attempts in the future. You can also do as the biker should yourself. Have a friend come by on their bike, letting the dog give chase, and the biker should then stop and stand to face the dog directly. Do this each time the dog tries to give chase to the biker and sooner or later they will get disinterested when they realize the biker is not going to try and flee from their chase. Installing verbal commands which stop your canine is going to be the best bet as far as things you can do yourself. Using rewards, train them to stop and stay on your command, and use these commands while your friend with a bike comes by. Continue to build up their reactions to your commands until they no longer try and give chase when they are told to stay.
Other Solutions and Considerations
Contacting a behavioral specialist or dog trainer is going to give you a big leg up on this. Dogs like to chase. For thousands of years, this is how they fed themselves and their human companions. In fact, until very modern society, we favored and bred the dogs that gave chase the best. We deemed these to be favorable traits as strong and fast hunting dogs meant more likely success on the hunt. It is only recently, in the last few hundred years, that humanity has really removed themselves from the need to hunt for their food source, and therefor removed our need for strong hunting like characteristics in our dogs.
If your dog chases down bikers, even though it may seem hilarious, it is rather mean and dangerous for the biker. Even if your dog has no wish to injure or harm the biker, it is important to contain or train the dog out of these impulses. It can be dangerous for your dog, yourself, and the biker most of all.