I'll bite...
My answer would be: this is an estimate, so we can consider the bubble to be a sphere.
The part that is soapy water will have a mass that is one sphere's volume minus a very slightly smaller sphere's volume, multiplied by some density.
We can approximate the density to that of water and so calculate that.
Now, is the mass of the soap bubble just the soapy part or does it include the air inside... I would argue it does include the air inside, so add the volume we removed from the soap volume back again, multiplied by the density of air.
so: something like M = ((pi.r³) - (pi.(r-δ)³) ) * λᵣ + (pi.(r-δ)³) ) * λₐ
where:
λₐ = density of saturated air
λᵣ = density of water
r = external radius of bubble
δ = thickness of soap wall
Areas of approximation:
- air pressure will change the volumes a lot
- humidity will change the density of the air
- the bubble is likely not a sphere
- the bubble wall is likely not of consistent thickness
In summary this is likely a very poor approximation.