Some ways to do that are:
- Mute with the index finger of your fretting (left) hand and use middle and ring fingers to bend. ...
- Use palm of your picking (right) hand to mute all strings above the sounding one. ...
- Muting with a thumb is another way. ...
- Cheat with a string muter if you don't use open strings a lot.
Why do my fingers go under the strings when I bend?
Re: Setup needed? Fingers going under strings when bending. In short: that sounds as if your string height (i.e. action) is too high.