When I bend  a string, my finger tend to go under the subsequent strings when I push the string but usually established guitarists push the strings with other strings and use their index finger to mute the unwanted strings from sounding. Is my bending technique wrong ? My index finger is short, I can't reach other strings to mute them. 
Amateur guitarist straight from the oven !

Sounds like you have insanely high action or microscopic fingers.  I don't think I could do this on any of my guitars if I tried. 
There's different ways to bend and to mute the strings - you need to use your left and right hand to mute.

That being said, your index finger is great for muting strings when bending with the third finger, but you don't have to lay it across the entire fretboard, just the top few strings will do the trick.