This is done by letting the lower string slip under your finger while you bend, which will allow you to fret that new string by just rolling your finger a little bit. This is done a lot in blues playing, but in that case the new string is already picked while it is still bent upwards.
What happens when you bend a guitar string?
String bending is a guitar technique where fretted strings are displaced by application of a force by the fretting fingers in a direction perpendicular to their vibrating length. This has the net effect of increasing the pitch of a note(or notes as the case may be).
Does it matter which way you bend a guitar string?
A good rule of thumb when bending is the low three strings (E, A, D) should bend down towards the floor while the high three strings (G, B, E) should bend upwards towards the ceiling. The two most common string bends are the half-note bend and the whole-note bend.