Before digital sound recording, analog sound quality was inferred from it's dynamic range, the ratio of sound from the loudest passages divided by the quietest passages. Vinyl records were often said to have a maximum theoretical dynamic range of as much as 78 dB. But in the real world, this number was more like 70 dB or less. Things like tape recording speed and magnetic tape particle density, as well as the inherent noise level in vinyl grooves tended to limit how low you could reduce the background noise level, thus limiting the dynamic range. The upper limit was created by the decision to run the turntable speed at 33.3 RPM and keep the recorded music to roughly 20 minutes per side. Efforts were made to increase this range, such as with DBX noise reduction. But it never took off at a consumer level.
Rather than estimate the number of bits in an analog recording, it might be easier to compare the dynamic range available from a CD once it's converted to analog. I don't remember clearly, but I remember a number close to 90 or 95 dB, a dynamic range much greater than 70 dB.