When you open the bottle and reduce the pressure you now have a supersaturated solution of carbon dioxide in water so it is energetically favourable for the gas to come out of solution.
However for the gas to come out of solution you have to form a bubble and the mechanism by which this happens is called nucleation. But there is an energy barrier that prevents tiny bubbles from forming, and as a result bubbles will only form when there is something to help them nucleate. For more on this see:
Anyhow, if you look carefully at the bubbles coming out of an opened bottle of soda you'll see they aren't forming randomly. Typically you'll see streams of bubbles coming from an area where there is some aid to nucleation e.g. a defect on the glass wall of the bottle.
This means the escape of the gas involves two steps:
formation of bubbles at a nucleus
diffusion of the carbon dioxide through the water to the nucleus
And it's step 2 that makes the escape of the carbon dioxide take a while. Where an aid to nucleation exists, e.g. at a defect on the glass wall, formation of a bubble will be very quick. However formation of the bubble will quickly use up the dissolved carbon dioxide in its vicinity and formation of further bubbles has to wait for more carbon dioxide to diffuse to the nucleation site. Diffusion of gases dissolved in water is surprisingly slow, and even though the gases typically only have to diffuse a few millimetres they still take a while to do it.
If you want to get the carbon dioxide out quickly the best way to do it is to increase the number of nucleation sites so you get many more nuclei and hence reduce the distance the dissolved gas has to diffuse. The traditional way to do this is to drop a mint into the bottle of soda, but stand well back when you do it.