To maintain the surface tension which formed our original bubble (in order to keep the bubble from breaking), we may change the temperature/pressure of air on both sides of the bubble varyingly, with different rates.
Is such a configuration possible? Examples of any such system?
The answer is YES. Note that pure water bubbles are unstable but it should be possible to freeze one without it popping as long as it is thick enough and the pressure is correctly regulated. (This video shows in detail a soap bubble partially freezing and then bursting on contact, and this video shows more completely frozen soap bubbles rolling around and eventually disintegrating.) If completely frozen, the bubble will no longer be a perfect sphere because the ice crystal will nucleate at certain positions and this will distort the surface.
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