Sometimes when I'm playing, I'll bend a string and simultaneously play a fretted note. When I do this, the fretted note sounds slightly 'off' or out of tune.
What causes this and how can I prevent it? Is it related to having a tremolo system on my guitar?
Yes, this is related to your tremolo--assuming you have a floating one (I haven't seen this problem on a non-floating trem). As you bend, the bridge moves as the tension on the string is increased. You could fix this by increasing the counterforce on your tremolo, and how you do this depends on they type of tremolo you have.
Yes, it's to do with having a non-fixed bridge.
The tension of the strings on the bridge (pulling the bridge toward the nut) is offset against the tension of the springs in the back of the trem unit. As you bend a not with your left hand (assuming you're right handed), you increase the tension on the front of the bridge, and this has the effect of pulling the other strings flat (the tensions at the front and back are no longer equal). Basically what is happening is the same as applying gentle downward pressure to the trem arm while playing a fretted not.
Sadly, it's a well known phenomenon linked with non-fixed bridges, and though there have been some clever technical responses to combat it, they tend to result in severe compromises.
