my fingernails are too fat and are not sharp enough to have them in place underneath the strings...so i tend to just use my index,middle and ring finger in place on one string and bend...

but i get an overlap of the other strings too (i normally bend the first string all the way to the third string),and when i unbend,the 2nd and 3rd strings are not muted...its really getting frustrating..
When I have to bend like that I'll usually make it coincide with an upstroke so I can hold the pick against the second string and the thumb can then deal with the third.
my finger nails are short...what i mean is,my friend uses his fingernails to mute the stirngs by digging under the strings with his nails..
I have a similar problem, just work on muting them with the palm of your right hand.
Fender Deluxe Strat HSS
Fender Standard Strat
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Epiphone Les Paul Standard
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Seymour Duncan Twin Tube Mayhem
Roland Microcube
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Korg Pitchblack
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Hohner 3/4 Classical
I like to have some nails on my left hand to get under the strings. I noticed everytime I cut them to short I can't bend as fluently