Personally I wouldn't use the Distance map for the bubble, it isn't really needed and adds extra calculations. Instead, use Max's Realtime Booleans. Should be fine so long as you are using cubes with a sphere to be cut out from them (more complex geo runs into issues, as with any booleans).
EDIT - also I am not sure the Distance map would then count as being "outside the geometry" as it is really just an effect of opacity on the object, not actually changing the geo, so Realtime Booleans may be a must in fact. It's how I have done it in the past.