As the pressure exerted by water is directly proportional to the depth of water, as the depth of water increases in a water body, the pressure increases linearly. So when a air bubble rises in water, the pressure acting on the air bubble decreases.
We know the that as the the pressure acting on gas is inversely proportional to the volume occupied by it i.e. if the pressure increases, then the volume occupied will decrease and if the pressure acting on the gas decreases, then the volume occupied by by the gas will increase.
In the rising air bubble, as the pressure is decreasing, the volume and hence its size increases.