And of course color is defined by the wavelength of light.
This may be more detail than you need, but color is not a phenomenon of physics, but rather one of psychology. Color is not defined by the spectral characteristics of the stimulus -- the wavelength(s) of light -- but by the human response to those stimuli. Since there is a large range of commonality in the way that men see color, and an even larger range in the case of women, we don't need people to turn spectra into colors; we can do it with sensors and tables formed according to the results of experiments on people. That's how light, a phenomenon of many dimensions, gets transformed into color, which has just three.
Before we can talk about the relationship of gamut to bit depth, we need to pick a color space, which defines the three axes. Let's pick sRGB. Think of it as a cube, with one corner black, one corner white, three corners each particular shades of red, blue, and green, and three corners equal mixtures of those that we call cyan, magenta and yellow. Those eight vertices, and the planes that form the faces of the cube, define the gamut of sRGB. It can't encode colors outside of that cube. You will usually see gamuts displayed in other than the color space under consideration, but Im going to ignore that here to make it simple.
Now to the bit depth. If the bit depth of each color is one bit, we can only encode the corners of the cube. We can only make one red, one green, one blue, etc. Now let's say the bit depth is two for each color plane. Along the red axis, we can have black, a dark red, a lighter red, and the full-on red at the corner of the cube. Same for blue, green, cyan, magenta, and yellow. We can also get four neutral-axis colors by setting R=G=B: black, dark gray, lighter gray, and white. There are other additional colors with different combinations of the two bits in each color plane, for a total of 64 possibilities. The colors in the interior of the cube don't increase the gamut of the color space measured in itself, but you could argue that the colors on the faces do or don't. That's where bit depth and gamut interact, albeit weakly.
If we use three bits for each color plane, we can make 8x8x8 = 512 different colors. With four, we can get 16x16x16 = 4096 colors. with 8 bits, it's more than 16 million. Also at eight bits, we have more than 65000 colors on each of the faces, and the weak interaction between gamut and bit depth becomes inconsequential.