I would assume that we need to convert log_{2} bits into log_{10} for dB and double it because of the squaring operation required to get power from amplitude. Constellations are two-dimensional, so we need to also have a factor of 1/2 in there.

So bits * 2 / 2 * 10 * log_{10}( 2 ) + some constant which I don't know the value of. That would be about bits * 0.3 * 10 + constant, ie bits * 3 + *C*. But I don't know what the assumed zero dB power reference is. Since SNR is a ratio, the constants will cancel out, so in that case isn't my constant simply zero?