I just ripped apart a microwave, and one of the things I got out of it was a turntable motor. This turns out to be a 5-watt, 5 RPM, synchronous 240VAC gearmotor. This is one of the few occasions where it really doesn't matter which way the motor turns, so in fact they used a synchronous motor that turns in a randomly different direction each time, depending I suppose on where it was when it stopped.
Even if you couldn't sense its position well enough to predict which direction it would turn at startup, you still might be able to use it for motion control with closed-loop feedback, using the following scheme: when you start up the motor, if it's going the wrong way, wait a random fraction of a rotation (of the motor, not the gearbox output shaft), turn it off, and, after enough time for it to stop, turn it on again.
You could take this simple control scheme one more meta level to flagellate bacterium behavior: while the conditions for a machine continue to improve, run the motor continuously; while conditions remain the same or get worse, run the motor intermittently. Connect the motor to a mechanism such that, in one direction of rotation, the machine moves in a straight line in whatever direction it's pointed, but in the other direction of rotation, the machine wanders around randomly. When the motor is running intermittently, it will sometimes go in a straight line, and sometimes wander, but once it happens to be moving in a straight line that improves the situation, it will continue.
Unfortunately, such a mobile machine would probably be battery-powered, and running a synchronous AC motor off DC requires about as much circuitry as the above feedback scheme would take to implement.