| The noise isn't from your amp. It's a combination of the natural compression that distortion creates boosting the noise already present in your bass, and additional noise from the gain stages of the pedals. The nature of dirt pedals is that they will almost always add SOME noise to your signal.
A noise gate like the Boss NS-2 is helpful in a situation like this, but it's not an end-all solution. I have one on my pedalboard, and I couldn't imagine playing without it at this point, but it does have a few drawbacks. The opening and closing of the gate isn't as natural as it could be, but that is in part because I have mine set for a really extreme gate. | 
