Does the sun blow a bubble into the interstellar medium?
At the moment, the Solar System is inside the Local Interstellar Cloud (which is itself within the Local Bubble). The LIC has a neutral hydrogen number density of $\sim0.1\text{ cm}^{-3}$, which is a bit lower than the mean galactic neutral hydrogen number density. The Local Bubble itself is less dense than the LIC, by about one or two orders of magnitude. On the whole, this region of space is less dense than the ISM, on average.

So, if we take atomic hydrogen density to be a good benchmark, then the LIC and surrounding regions are in fact less dense than the Solar System on average.