Yes there is a terminal speed of air rising, similarly to an object falling has a terminal velocity.

With an object falling it's the the point at which acceleration due to gravity match deceleration due to air resistance.

For a bubble rising, this is the buoyancy counteracted by drag created by the liquid. So different gasses would move at different speeds though different liquids based on their viscosity.

The issue is that this drag amount is changing constantly. There will be flows and slight variations in density. The bubble will likely split well before it reaches maximum velocity.

A large bubble will deform into a more streamlined shape allowing it to rise faster, this same deformation is also what breaks it apart. The smaller the bubble the more stable it is and the more it's likely to reach terminal velocity.