Not to be difficult but when you say "bore volume" do you mean "bore diameter" or the volume of, say, the throat/leade? Thinking about it a bit more, you are probably saying the entire bore because the gas is still expanding behind the bullet all of the way to the muzzle.
Correct, we are talking about the full volumn of the bore, minus the chamber. Obviously, the concept of expansion ratio has limitations. If we substituted the volumn of a 16 barrel for that of a 24" barrel, we are going to get a different answer. As well, as you surmised, bullet weight also plays a role. The typical approach to bullet weight is a faster power for lighter bullets, slower for heavier.
Again, fast and slow are about how quickly a powder reaches a peak pressure, not about how "fast" it burns. It is pressure that most effects velocity. Note how much more powder it takes for the 300 Win. Mag to reach it's velocities as compared to the 30-06 with the same bullet weights even though both operate at similar pressures.
A lighter buller (for caliber) travels faster, takes less pressure to move up the barrel and has a similar effect to increasing the expansion ratio. This lets us use a faster powder. Conversly, a heavier bullet moves slower and takes more "oomph" to get it moving up the barrel, so we want a powder that reaches the peak operating pressure a little slower.
The 30-06 case is an exellent case to use to study this. Also note what happens when that case is shortened to a 308 and the same changes made (ie look at 243/7-08/358 Winchester) and compare the powders used. Also look at the relative bullet weight for caliber and how the powder speeds change with them as well. Also, compare the powders of the '06 based cases with those of the -08 based cases caliber for caliber (ie 270 with 7-08 35 Whelen with 358 Win etc)
This is a good question and deserves a better answer than I am able to give, keep asking questions like this and you'll be come a truely accomplished reloader.