Ok you have this backwards. Think of it like this.
You go looking for crayons. You find boxes of 6 crayons, and boxes of 12 crayons. The number of crayons in your box is the bits. This is the number of possible discrete colour values you can have. In an 8bit image you have 255 shades of red, green, and blue in combinations, or 16.7million crayons. With a 16bit image you have 65535 possible shades of red green and blue in combinations, or 281.4trillion crayons.
Now getting these boxes from different manufactures you may end up with different colours.
One manufacturer's box of 8 crayons may have: Steel blue, sky blue, sea green, olive, brown, orchid, white and black. These are generally dull colours and would be comparable to sRGB (a small gamut)
Another manufacturer's box of 8 crayons may have: Deep blue, Cyan, Green, yellow, Red, Magenta, white and black. These are very bright and pure colours which would be comparable to a larger gamut like (AdobeRGB).
Both only offered you 8 colours but one's colours are much more pure. But notice that the one with more pure colours is missing some like brown, olive, etc? This is the result of using a wide gamut with a small bitdepth. Not every colour can be represented.
To tie this all back together. Look at the very top chart. This is the CIE1931 chart and the horsehoe represents all the visible colours at full saturation the human eye can see. The triangles represent the gamuts that can be made by combinations of a certain value of red, green and blue. The closer to the edge of the horseshoe the more pure the colour. The number at the edge is a single wavelength, and if you've ever worked with high quality lasers, or a high quality diffraction grating, that's the pure colours we are talking about.
If you want to see a colour that can't be displayed in sRGB look at this diagram I whipped up in photoshop:
http://www.garbz.com/colourwow.gif Take note of the red colour in the left image, now move your head close to the screen and stare at the white dot for about 30 seconds or so. Now take your head away and gasp in the glory of the amazing saturation the cyan now has. This is not a colour you can reproduce on your screen.