What is the braking (stopping) distance for bicycles?
The stopping distance is a factor of:


Reaction Time
Speed and Mass (bike, rider, and load)
Efficiency of Brakes
Braking force applied (on which brakes and how applied)
Road/track surface (including water, ice, gravel, manhole covers etc aspects)
Tyre width, grip, tread etc


You have to notice a need to brake, move your hands to apply braking force. Then physics comes in, a bike of a given mass moving at a given speed has a certain amount of inertia that needs to be overcome and how much you squeeze the brakes.

So it's going to vary massively by bike/rider/situation.

The same is true of cars. Top Gear (UK) demonstrated a few seasons back the UK Highway Code approved braking distance at 60mph for a car, then showed how a reasonable car could go from 100mph to a full stop far, far, far short of that distance.

It's trained as a rule to car drivers because of the significant damage that can be caused with a big heavy lump of metal moving fast, based on very old figures.

I doubt any country enforces it on cyclists. And road cyclists in cycling groups routinely ride on each other's wheels to get the benefit of drag etc. There training and skill will come in.

Generally, the practical rule trained out in the UK for motorists (and I've been (un)fortunate enough to be required to attend a driver skills course following an incident plus opted to attend some advanced motorcycle training) is the 2 second rule.

Keep a gap of 2 seconds between you and the vehicle in front. That allows you to stop in a controlled fashion. if someone is sat close behind you, expand your stopping zone to buffer their lack of stopping zone. Increase to 4s in the wet and 20s in icy conditions.

On top of that, when it comes to bends, always make sure that you can stop in the space that is visible, so you naturally have to slow down as the road bends.

That said, keeping a 2s gap in a cycle commute is going to have the car behind you putting you at risk!