Can you freeze a bubble?

Haha you can freeze some water when there are air bubbles within it so the ice retains bubbles...but that's not what you asked...

If you mixed together two imiscible liquids, you would get bubbles of liquid A inside liquid B. You could then lower the temperature until you freeze the "bubble". e.g. olive oil and water. Yeah I know that's not really what you meant!

Nice question! As said, you can freeze the medium contains the bubble. And bubbles are formed by surface tension and this surface tension depends on temperature. Soap bubble balances surface tension forces against internal pneumatic pressure. So when you change the temperature, this equilibrium changes, and the bubble breaks. So my answer to your question (what you meant) is NO.

I would think that, if you bubbled some CO2 gas into a container of liquid nitrogen (at -196°C), the CO2 bubbles will freeze to solid CO2 and fall to the bottom of the container..

NO, If you try to freeze a balloon the gas inside will contract and therefore shrink, the same idea would apply to a "soap" bubble. If it did freeze it would be only for a fraction of a second before the surrounding pressure breaks the ice.