When frying with oil, it's generally assumed that heavy bubbling indicates frying, and little to no bubbling indicates a lack thereof. What's the connection between bubbles and frying? If you create bubbles in some other way, baking soda and vinegar in oil perhaps, will you increase frying?
I am extremely skeptical that a typical cooking oil and water form a significant azeotrope. Such a claim demands an authoritative reference. Most known azeotropes have boiling points only fractions of a degree below the lower boiler, making little difference in the boiling point. Likewise, most known azeotropes contain over 99 wt% of the lower boiler again making most azeotropes insignificant.
It is simply my opinion, but I believe the oil transported from the bubbling liquid is in the form of an aerosol or perhaps even larger droplets.
Those issues aside I agree the bubbling is boiling of lower bp chemicals, almost certainly mostly water. As cooking occurs, decomposition into lower bp compounds is possible (and if significant amounts form, they may form azeotropes with the oil (but see comments above)).
I am also not aware of the solubility of the various atmospheric gasses (N2, O2, CO2) in oil. Gasses are in general less soluble as temperature increases (eg carbonated beverages), so they also would boil out if present in significant amounts (I'd guess they aren't very soluble at 1 atm pressure).
I should also add that while most azeotropes aren't "significant", most liquids do form them.
EDIT: This is very probably wrong, and to be considered so unless someone can find a reliable source for these claims. See @Li Zhi's answer to know why.
The bubbles are not the cause of the frying, but its consequence.
The main purpose of frying an aliment (apart from cooking it, of course) is to remove its moisture. It does so by boiling the water away. Hence the bubbles.
To delve a bit on the technical side, the water/oil mixture probably forms an heteroazeotrope. This means it is not water which boils, but a mixture of (mostly) water and (a bit of) oil, with a boiling point below either. This is why frying things is so messy: you actually "boil" oil which recondenses into droplets that cover everything around, like some disgusting, greasy morning dew.