In order to blow a bubble, you have to push the liquid out of the way to make room for the air. In order for air to push, it has to have pressure. The harder it is the push the liquid, the higher pressure the air has to have in order to successfully push.
Viscosity is just a measure of how hard it is to push liquid around.
The question about “is it harder to blow bubbles in deeper water” is a bit tricky, because it depends on how you do it.
If you stand at the surface and have a long straw that you’re using to blow bubbles, then yes, it’s absolutely harder to blow bubbles as you get deeper. This is what I think you meant by “depth of the liquid relative to where the air is released”.
If you’re a scuba diver trying to compare blowing bubbles at the surface vs 100ft down, then the comparison more complicated. It will be harder to do it farther down, but the magnitude of the effect will be much smaller than the straw example. Further it’s my understanding that the change in difficulty isn’t exactly from the depth, rather as you go deeper the viscosity of the water and of the gas in your lungs is going to increase, which makes breathing harder.
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