Nope, it's not the weight of the bike, but the strength of the bike that will make the difference. Some of the force will be taken up in the crushing of the front wheel, yes. But the bike would become the pivot point, and is strong enough to exert well over 175 pounds of force (deceleration) on the bicyclist if he were to keep has hands on the bar. It doesn't have to weight that amount, just exert that amount of force. Are you suggesting that in this case, linear momentum is not conserved?

By the way, there is an outside force acting on Newton's Cradle--the person who lifts the ball initially to begin the process. That would be analogous to the pothole, or in this case the other bicyclist, in this system.

John