Yes, your method is a perfectly good way of measuring viscosities. It's a bit limited because it's hard to measure the bubble diameter exactly, but assuming you can do this you can calculate the viscosity of the fluid using Stokes' law.
However note that I haven't mentioned yield stress. That's because yield stress is a slippery thing to define. Indeed a rheologist friend of mine, Howard Barnes, maintains that there is no such thing as a yield stress. The problem is that for non-Newtonian fluids the viscosity often rises very rapidly as the shear decreases and it may get too high for you to measure it. So how do you you tell the difference between a true yield stress and a viscosity too high for your equipment to measure?
If you shake up your non-Newtonian liquid to get some bubbles in it then come back in an hour or so you'll see some apparently stationary bubbles, and you can use these to calculate a "yield stress". But if you come back a bit later you may find the bubbles that you thought were stationary have moved a bit. You could wait a bit longer, but you can't run the experiment for very long because Ostwald ripening will be changing the bubble sizes as you watch. That means there's inevitably a limit to how high a viscosity you can measure. Unless the yield stress is below this limit you won't be able to measure it.