For very small bubbles, we can show that the speed of the bubble is
u = 1/3 a^2 g/nu
where a is the radius of the bubble, g is the acceleration of gravity (980 cm/s), and nu is the "kinematic viscosity" of water (0.14 cm^2/s).

This only holds for bubbles less than a millimeter across. When they get bigger than that, a "boundary layer" forms, which changes the way the water flows around the bubble, and the speed of the bubble is closer to
u = 1/9 a^2 g/nu