Bass- at what frequency does it change from sounding like a string to just a low tone?

Strings produce a bunch of different frequencies that make them sound like a string. The technique used to vibrate the string changes the frequency profile, if you will, of the sound. A hard pick produces different frequencies than fingers, etc.

One good example song is "Snuggle Up" by Brian Bromberg. If your low end is clean and clear enough, there’s a lot of very low frequency pitches mixed with textures on top from fingerstyle playing with muted plucks. A pure synthetically produced sine wave at the same fundamental frequencies would just sound like pure tones, without the overlaid textures.

The basic method mentioned by @erik_squires is going to be the most productive for most people. But you can get an idea of what your low end frequency response curve might look like by using something like the "Tone Pak" by Bass Mechanik just to get an idea of general areas where your bass is to loud or too soft. It’s basically just level normalized test tones from 2hz to 50hz. Tedious, but helpful and ultimately educative for most people, I would think.

Note: don't keep a single sine wave going at even moderately loud decibel levels for an extended period because it can damage your sub.

Yeah, almost no normal person is going to choose a ruler flat response. It’s really only an hypothetical ideal. We all have preferences which are also affected by offensive acoustical issues.