Is there any data that declares the (approx) ascent rate of the smaller the bubbles and if depth has an effect on that rate?
I'm sure there will be data if you are prepared to read a few very technical articles. I remember back in my varsity days we did touch on bubble hydrodynamics and I remember the professor saying that we'd discuss the essential principles but that bubble hydrodynamics is a very complex field with a lot of poorly understood variables.
The upward velocity of a bubble is affected by a number of things, obviously it's buoyancy (which is a function of its size), but also by the viscosity of the medium in which it travels, the amount of impurities (surfactants) present, the temperature (not sure how), the shape of the bubble (they're not all spherical), turbulence in the water, presence of other bubbles etc. etc. etc. Also, bubble of micrometer size act differently to these factors than bubbles of medium sized. The bubbles we are talking of (those that form when we exhale under water are considered medium and large sized). The bubbles causing DCS are considered micro-sized.
But to get back to basic principles, you could say that the upward velocity of a bubble is mostly affected by the buoyant force on it - which is a direct function of its size, explaining why larger bubbles rise faster than smaller bubbles. That said, bubble grow as they rise because the ambient pressure decreases and the volume of gass remains the same (remember Boyle's law).
So yes, the same bubble will rise faster at shallower depth but it hasn't really got as much to do with the depth as it has with the size of the bubble. Or put this way, the same bubble will rise faster in shallower depth because the bubble is bigger, not because the ambient pressure is different.
If you release two bubbles of equal size at different depths, they should rise at the same initial velocity. The buoyant force is determined by Archimedes' principle which states that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. Seeing as water does not compress, the weight of a certain volume of water at 10m is the same as the weight of that same volume of water at 1000m.
I hope that answers your question. If you're really interested in the fluid dynamics of bubbles you can look at
this article, or
this article, or
this one but don't say you haven't been warned. These things are complicated. The last one is perhaps the most easily understood by laymen like me.
Getting back to this assertion that you should not ascend faster than your smallest bubbles, I'd be curious to know whether there was any study behind it or if it just sounded reasonable. Like you, I'd be interested to know just what the typical ascent rate of a small bubble is and how that compares to the 10m/min I've been taught (or whatever other agencies teach). But mostly I'd like to know, exactly WHY, should I not ascend faster than my smallest bubbles? But somehow I don't think that question really can be answered.