The water bottle does not work for problems like this
A LOUD NO or OUCH is much better  even a hiss can work when she tries this.
You have let the problem go on so it will take a little while to stop it
The kitten is becoming over stimulated when you see her going for her hand
drop the toy and use the loud NO or OUCH

Worse comes to worse you can wear a glove or coat your hand with something
that taste or smells bad such as bitter apple or citrus smell

For me I use a coffee can full of marbles when one of my furballs does
something wrong.  They hate that noise and know when I reach for it they
have done something wrong  and stop immediately

Phantom my oldest used to do this I let it go on for a long time thought it
was natural for them to do it.  I used the Ouch before I learned about the
marbles.  Phantoms still nips but only enough to let me know he is there and
than he licks my hand when he nips.  The nip is only enough to put pressure
on the skin the only time he has ever drawn blood was when I pulled away to
quick.

Kittens have their own language, so you have to "speak it" to make them
understand.  When she bites, make a *very* high-pitched "MEW" - that's
kitten talk for "uncle" (when two kittens are play fighting, and one issues
that "MEW", the other will sit back and give it a break before starting to
play again)!  That should stop her immediately - then take your hand away
and give her a "time out" by not playing with her for a few minutes.  *Then*
try to distract her with a wand toy.

Hugs,

CatNipped