I've read that the difference is so slight that any movement of air causes the CO2 to mix with it. I would think that since CO2 is still a gas it would rise, maybe not as fast as other gases, but still rise nonetheless.
pressure and diffusion. as the co2 builds up the pressure increases, and since it wants to reach equilibrium itll be forced out of the bottle. diffusion works the same way. the co2 concentration in the bottle is higher and it wants to reach equilibrium so it moves into the water.