I spend most of my practice time on two Strats with different setups. One has 10-gauge strings with low action and a thin neck. The other has 12-gauge strings with high action and a thick neck. (Guess which one destroys my fingers.) Whenever I pick one up after leaving it out of the picture for a while, I notice that my bending technique doesn't work anymore.
There's a subtle trickery to bending notes that I don't hear mentioned often. It involves how the adjacent strings are pushed aside. In most cases, the only note you want to hear is the one you're bending, (Jimi's wide vibrato on the "Foxey Lady" intro is a notable exception.) Problems abound if an adjacent string burrows under your fretting finger in the middle of a bend. If you try to pick the bent note, you could easily hit the unwanted string, and it will probably sound awful. And if the adjacent string snaps into said position, it will sound on its own like a tiny cry for help from an amateur guitarist.
I've found a few ways around this. The most obvious is to keep adjacent strings out from under your fretting finger. When bending toward your face, let the adjacent string get stuck in the flesh at the tip of your finger, just under the tip of your fingernail, keeping it off the frets. If the action is high enough, you could get your bending fingernail(s) completely under the other strings. When bending toward the floor, adjacent strings should get stuck the same way in the pad of your finger (not the callus but right in the center of your fingerprint), keeping them off the frets.
If the action is too low for the above methods, then adjacent strings will inevitably be fretted during bends. The tricky part is to keep these unwanted notes silent. The strings on my low-action guitar are still high enough that I can sometimes hold adjacent strings off the frets, but they frequently snap from the fleshy tip of my finger down to the fretboard under my fretting finger. The best solution I see is easing the other strings under my fretting finger as I bend. If I'm bending toward my face with my 2nd or 3rd finger, I'll use my 1st finger to guide the other strings under my fretting finger. They won't snap into place, but I gotta be really careful about avoiding them with my pick.