Gamut is how saturated the colors can be at their most saturated.
Bit depth affects how many tonal steps there are between unsaturated and saturated colors, ie. how fine of a gradient you can make.
The two issues aren't really related to each other. The difference between 8 bit and 10bit display is very, very subtle and questionable whether it is even visible in most circumstances, since it's the difference between 16 million colors and a billion colors (both more than your eye can see). Most professionals are using 8 bit workflow with wide gamut monitors with no problems at all.