I hate this. Example: I bend the B string. When i release it, I always get a slight sound from the D string. If I bend the high E string, I get a sound from the G string. I've tried every possible position, and still nothing helps. The bridge is also very rusty, I have't changed the strings in months, but I doubt that would help. I have a VERY crappy guitar.
mute it with your palm maybe?
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Everton FC
its all about muting. it just takes practice. im still not perfect at it but im a lot better at getting rid of that noise than i used to.
Lightly mute the strings as you're releasing.
Sounds like a lot of people have a problem with this... Maybe it's time I make a video tut.

Or you could go all panzie Synyster Gates and put a wristband on your (guitar) nut.

Oh, and it's not just your crappy guitar. All axes do it to some extent.

Try to bend with your middle finger with your 1st and 3rd finger slightly touching the strings you don't want to be heard. Of course, you can't always bend with your middle finger, but this is quite helpful when you do
Its all about muting. Whether or not to do a palm mute to prevent the noise or a mute from your fretting hand all depends on your playing skill and the type of stuff your playing. Whatever lick your playing, play around with different muting techniques until you get the most comfortable method.