Elements of answer:

It is not an easy question, as we lack of data to constrain strongly the density and mass of Saturn's rings.

However, a first clue of their density is their optical depth (that is a measure of the transparency of a medium). The densest rings are the one of the main ring system (rings A, Cassini Division, B and C) plus ring F; they are characterized by optical depth larger than 0.1 (up to about 5 for the densest part of ring B). Rings in the faint ring system (E and G) have very small optical depth (lower than $10^{-5}$).

With this regard, B is indeed the densest ring of Saturn's rings. (edit) Looking around ([1] and [2]) you can find numbers that help to figure out the density of this ring. Knowing its mass (about $2.8\times10^9$ kg) and its extend (from 1.527 to 1.951 Saturn radii, with a typical thickness of 100 m), you can deduce a mean density of about 0.0167 g.m$^{-3}$ (about $10^5$ times less dense than the terrestrial atmosphere at sea level).

Just for fun:

This gives you an idea of what means the optical depth. In the densest parts of ring B, optical depth is between 2.5 and 5, so you'll definitely notice you're in the ring. It is probably more complicated than that (with ring particles ranging from dust size to house size), but you get the idea.

Side note:

Optical depth is a measure of transparency of one medium; it measures how radiation is neither scattered nor absorbed by the medium. It expression is given by

$$\frac{I}{I_0} = {\rm e}^{-\tau}$$

where $I_0$ is the source intensity, $I$ the observed intensity, and $\tau$ the optical depth.

Sources:

• Charnoz 2009