0.01 > 1 [bit] / 2^n [total_bits]
The n integer that solves this equation is the minimum number of bits you need. Each bit represents a step in value, and 2^n is the number of bits that represents the largest number (the full scale).
The speed of the DAC is also a factor in sound quality (it's pointless to have a few very accurate beeps and not have any of the sound in between).
A DAC with n bits can output 2^n discrete levels.
It's pretty simple for resolution. Just think, if 2^n bits is the maximum number of bits, then 2^n bits also represents my maximum measurable value of say voltage, sound, light, or whatever), then that means each bit represents
[maximum value of voltage/sound]/2^n units of voltage, sound, etc. That's your resolution. I think you have lulled yourself into thinking it is more complicated than it really is.