don't know if the warp bubble is in subspace, so much as it interacts with it... subspace is sort of a vague term, in that i think the most we know about it in the ST universe is that it doesn't obey the laws of physical space. since matter can never reach the speed of light in "normal" space.
sometimes subspace is referred to as a different "plane" of space. i think the original intent of warp drive (ToS era) was that the drive actually warped the space around the craft pulling the space as it traveled through which correlates to the various images that are often related to the warp bubble. you could even say the ship is stationary while space is moving around it...
http://science.howstuffworks.com/warp-speed3.htmi don't really understand the argument, though, sure there are differences and there are also similarities.