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.