According to Newton's law of motion, an object that is in motion will not change its velocity unless an external force acts upon it. In the case of a bicycle, if it is in motion with a certain velocity, it should not come to rest unless a force acts on it. In practice, we see the bicycle come to rest after a while. Does a force bring the bicycle to rest?
It's important to first understand that there are most certainly "external" forces, i.e. gravity, air resistance, and friction (due to the gravity of course). So, the simplest and quickest answer here is that air resistance and friction bleed off energy from the initial Kinetic Energy (the forward motion) of the bike. Eventually the bike wont have enough KE to keep it upright and it will fall and come to rest. (the question of what keeps it upright when it moves fast enough is a separate issue)
I hope that helps.
Let us consider there is no external force and the tyres are rolling smoothly without slipping. Here friction doesn't come into play let me explain you how.
Even if friction is present, this friction is not the answer. The concept of friction most books provide are deficient. The term "rolling friction" is also a misnomer.
The correct answer is rolling resistance for which the word "rolling friction" is often used creating confusions.
Let me explain you where it goes wrong(I have provided one link explaining rolling motion and correct concept of friction at the end of this answer):
Consider a wheel rolling smoothly. what is the direction of friction force? We might think it must be opposite to the direction of motion thats why it will stop after some time. But, this friction force is providing a torque also making its angular velocity to increase. So, we might think we took the direction of friction force wrongly. So, we take the direction of friction force to be in the same direction of motion which again gives wrong result. Here is the paradox!
Here comes the role of normal reaction. The contact between the wheel and the surface on which it is moving is a surface. This surface is formed due to deformed shape of either the wheel or the surface on which it is moving or both. On that surface the normal reaction on the forward portion of the surface is more than the backward portion, since the wheel is moving forward, giving a torque to the wheel in counter-clockwise direction.
Wheel rolling to the right, with surface deformation. The deformation is greatly exaggerated. Normal force components across the deformed region are not uniform in size. They are greater on the forward side, producing a counterclockwise net torque.
This results in slowing down the speed and eventually comes to rest.
Please read this: https://www.lhup.edu/~dsimanek/scenario/rolling.htm
The tyres of the cycle are rolling and the remaining cycle moves with a velocity same as that the centre of mass of the tyres have. Now the question is which force is responsible to bring the cycle at rest. The answer is Air-friction and Rolling-friction. It should be noted that the static and kinetic friction does not come into the picture because the point of contact of the tyres is always at rest w.r.t. the ground.
The friction keeps on acting until the velocity of the cycle doesn't become zero. Newton's Law's are completely valid.