Hi Sharke,
I'm not sure what John is referring to regarding stereo and mono, but the phase button just flips the positive and negative aspects of the waveform in a track. Easiest way to see this is to take a track with some audio on it, hit the phase button, bounce to a new track and zoom in. You'll get something like the following, where the track on top (in green) is the original and the one on bottom (orange) is the new, phase reversed, track. Notice how every time the waveform goes up on the top track it goes down on the bottom:

If I play those two tracks separately they likely sound the same, but if I play them simultaneously the result will be silence...summing two identical tracks whose phase are exactly reversed results in silence. This is the crux of null testing (a method of finding out if two tracks are the same).
The phase button is most commonly used when handling multi-mic'd instruments. For example, when dealing with a top snare mic and a bottom snare mic one of them will pretty much always need to have it's phase flipped.
So in your application when you have a single track, with or without a bass amp, and flip the phase you end up not hearing a difference. But if you have a second track that you are playing along with the first track and you flip the phase on one (and only one) of them, you'll hear a big difference. The two are being summed and thus you're hearing the results of an additive process.
It's certainly not required/customary to flip the phase when re-amping like that, at least not the way it is with snare drum mics, but it's absolutely something you can try. Sometimes an amp or plugin will affect the sound in a way that brings it out of phase with the original and you'll want to hit that button. Sometimes you'll want to do it to intentionally bring two tracks out of phase with one another, just because it sounds good. Sometimes you'll even want to flip the phase on only one channel of a stereo recording because it changes the sound in particular ways (that's actually a kinda common technique but be careful, it can cause mono compatibility problems). The "required rules" regarding phase, such as they are, are really only for multi mic applications and testing. Anything else is just creative use.
Good luck,
Dean