With the flip fluids addon for blender, its possible to do this, setting a low viscosity amount and then on the collision setting set the whitewater influence to 10 or more and then you can set that only the bubbles are displayed in the advanced panel in the domain and also setting the bubbles drag coefficient to 1 so it follows the surface.
The min/max energy speed and min/max turbulence values are set to [0.00, 0.01]. This creates a very low energy threshold that generates bubble particles evenly throughout the fluid in the first few frames of movement.
The Emitter Generation Rate is keyframed down to 0 to stop whitewater particle generation.
To fill the shape with bubbles more closely to the edges of the fluid, increase the Foam Offset value, which will raise the level of the Bubble-Foam layer that differentiates between bubbles and foam.
This will likely generate more particles than you would want, so to decrease particles you can lower the Wavecrest/Turbulence emission rates. The amount of particles to render can also be controlled in the FLIP Fluid Display Settings panel (The example is set to 1%).