If your next note is on a lower (i.e., thicker) string (what you call "the string above"), then you could use the same finger that you use for bending. 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. This will give you the effect of bending the higher (sounding) string, and then releasing the lower (sounding) string.
When the next note is on the higher (sounding) string (i.e., the thinner string), you would normally use another finger, namely one with a higher number (I'm talking about conventional fretting hand finger numbering). E.g., if you bend with your 3rd finger you would fret the next note with your 4th finger, if you bend with the 2nd finger you fret the next note with your 3rd finger, etc.