You can bend a string using any finger, what finger you use will be determined by what finger you play before or after the bend.
FIRST FINGER BEND: listen to the audio example and look at the tab of this riff below and you can see and hear that it would be impractical to play it any other way. This is because of the 5 to 7 hammer on (H.O.) with the first two notes. When using the first finger in this example you can either bend up or down (I prefer up).
This riff is using the A Minor Scale - Pattern 1
Bending using your 1st finger is difficult because you can't get a finger behind it to help strengthen the bend.
SECOND FINGER BEND: Using this finger is a little easier than the first because you can place a finger behind it to strengthen the bend.
THIRD FINGER BEND: This is the most common finger to use when bending. A lot of riffs use this finger when adding a bend to the solo. The riff below is the most common used.
This riff is using the 1st A Minor Pentatonic Scale
To play this riff, look at the image below. You can see that the 3rd finger is on the 3rd string 5th fret (the 2nd finger is also on the same string to give the bend extra strength) and the 1st finger is lying flat across the 1st & 2nd strings.
FOURTH FINGER BEND: This is very uncommon but still it is possible and sometimes necessary to do. It will feel awkward to do, once again use one or two fingers behind the fourth finger to give extra strength.