But what would cause the bubbles? If the inert gas pressure in the tissues is the same as the ambient at the surface, what would drive those bubbles to form? There is nothing coming out of solution.
But ambient at the surface has nothing to do with this particular process that I am describing. The driving force is the drop in ambient pressure on ascent. Your tissues don't "know" what is happening on the surface when you ascend to a shallower depth, they just experience a drop in ambient pressure. And unless you are breathing 100% O2, there is always "something" to come out of solution, that something is inert gas (N2 for the OPs question).
Here are two thought experiments to better illustrate this.
1) You have a cylinder with a piston and some amount of dissolved N2 in solution, and a gas-liquid interface, in Henry's law equilibrium. Let's say the PPN2 is 0.79. The piston has the cylinder pressurized to 5 ATA. You suddenly drop the piston, resulting in a sudden drop in pressure to 2 ATA. Gas will come out of solution, even though the PPN2 is the (arbitrary) value found in surface air.
2) Lets say that oxygen toxicity doesn't exist, or that we are doing this with some animal model with no CNS to make it an issue. This is just about bubble formation. You are at 330 FSW (11 ATA), breathing EAN93, which gives you a PPN2 of 0.79, the same as on the surface. You suddenly ascend with no stops to just below the surface. Do you feel that there is no decompression risk, no bubble formation? Remember, your tissues don't "know" what is on the surface. They just have experienced essentially an explosive decompression, and they have N2 in them.