How can I add bubbles to glass shader without using particle system?

Question

I created a glass object following this CGMatter's tutorial

https://www.youtube.com/watch?v=Zu74ljrLz4w&t=124s

Now I would like to add bubbles inside the glass, but since the glass object is a curve with a screw modifier I can't apply a particle system to make the bubbles.

The object is also animated, so the curve can't be converted to mesh.

How do I add bubbles to this glass object that also changes shape?