A few ideas...
Play the correct pitch with a non-bent 'reference' note and then compare your bent note to that. Do this over and over attempting to match the pitch as closely as possible. For the high E bend in the Sandman solo, if you have a 22 fret guitar you might need to hit a harmonic over the point where a 24th fret would be to get your reference note.
Use three fingers:
You should be using your first three fingers for the bend you are talking about. The work of bending the string should be shared by all three fingers, not just the 3rd finger.
This has two advantages: 1. You have three times as much grip on the string, therefore you can hold the string more lightly and still get the traction you need against the string, but with much less friction between your fingers at the frets/fretboard and your string against the frets/fretboard. This will also reduce wear on your frets.
Clean your guitar:
If your guitar neck is covered in sweat, dust or other smeggy residue you should use a guitar cleaner. Its easier to move your fingers against a clean lightly oiled fretboard.
Clean or change your strings:
Dirty/rusty strings will rip your fingers to shreds. Make sure you can slide your fingers up and down the strings with maximum smoothness.
Suck your fingers:
Your calluses should be nice and thick, but they should not be hard. In order to play comfortably all day your calluses should be pliable. So they bend around the string instead of cracking/cutting. I find that if I get hard calluses, sucking on them for a bit softens them up. You might find moisturiser works, but I prefer to have dry clean hands when I play.
Practice with four fingers as well:
(This is something I'll have to admit to being very slack on). But often you want to bend at the end of a passage that ends on your pinky finger. In this case it's advantageous to be comfortable bending on your pinky.
Ultimately you should be able to learn to bend any gauge of string (within reason) easily with practice. Then you can base your string choice on tone and durability factors.