Ok, so, imagine you had a one-stringed violin, except that rather than press your fingers on the string, you used a lever, kinda like a whammy bar. Does anybody know of such an instrument? Otherwise, there's a possibility I'll end up making one.
As pointed out, a washtub bass is what you are thinking of: https://en.wikipedia.org/wiki/Washtub_bass
Though the most common way to play it is to pluck the string, I have seen it played with a cello bow. The sound difference is instead of a steady thump, you get a cello like sound, but with a more primitive rattle.
You seem to be talking about a Brownie Bass: a wooden box with a thick neck, similar in size to an upright bass. The single string is fastened at the butt, passes over a bridge, and the other end is attached to a cam at the top of the neck. The cam is rotated by a short lever. As the cam rotates, the string is stretched, changing the pitch. If you use a regular upright bass string, you can get about an octave and a half out of the string. It can be plucked or bowed. The advantage of a Brownie bass is that the tone is clearer than a washtub bass, but requires lots more work to construct, though nowhere near as much work as building a bass viol, a project better left to a professional luthier. I've seen and heard a Brownie bass, but never personally built or played one. I play a washtub bass.
Many years ago I built a one-stringed instrument which didn't have a whammy bar, but similar: you pressed the string down in a trough between two glass rods at the top of the neck, thus changing its pitch.
While fun, it had severe limitations: the useable range was only about an octave, it was very difficult to control the intonation (especially at the bottom of its range) and the string had much less tension at the bottom (a fourth that of an octave higher), making it weak. But don't let me discourage you.
The crychord is a single-stringed instrument used by composer Harry Partch (1901-1974). The website harrypartch.com says the crychord was invented by "a student at the University of Illinois". The instrument has a single string whose pitch is adjusted with a lever, but rather than being played with a bow, the string is hit with a stick (although I don't see why it couldn't be plucked or bowed).
And a video where you can see one being played here (youtube.com).