I seem to have a problem with string bends. I can bend down, (down as in towards the high E, not down in pitch) fairly well, apply vibrato, etc, but when I try to bend up, I can't seem to control the string very well, and I can't apply vibrato to the note.

Does anyone have some tips, maybe a video showing correct technique?
Hm, well first for future reference the 1st string is High e. Lowercase, it's just so we know you're not confused between Low and High. No big deal

When I bend up, if i'm on a highfret...usually past 12 I find it easier to fit the neck into the gap between my thumb and index finger. And have my fretting fingers pointing towards the bridge going diagonal so it creates a pivot point where I can bend up or down and vibrato very easily. I notice a lot of well-known guitarists do this.

I use it as a "Switch" type of deal. I'll play normally then when I know i'm going to vibrato or bend I'll switch to the pivot position then switch back.

Hopefully this is not to hard to understand. Watch some Paul Gilbert videos.

Try using more than one finger.
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use like 3 fingers, and putting your thumb up higher behind the neck helps to give you more leverage. also, to bend up say a step and then add vibrato just takes a lot of practice to get the feel for it.
I forgot to mention I have been using 3 fingers, for both up and down. I couldn't even vibrato a note by lifting it up at all, much less after a bend.

Watching a Paul Gilbert video seems to have helped, I'm making a little improvement.