don't wake her up as this will annoy and frustrate her.
If you want to handle her but get scared of her bites instead of picking her up put a tube in her cage, like a cardborad one form the inside of a toilet roll or kitchen towel and wait untill she goes in it. once she is in pick up the tube and gently angle the tube so she slips out onto your hand! its how i get strangers to pick up mine - just in case. also rub your hands with a splash of lemon to rid any food smells. Also when she is used to your smell and handling pick her up by placing your hand on the bottom of her cage flat so she can sniff and walk onto it. maybe put a treat onto your hand!
hope she isn't biting anymore now though and this might help if she is!
Can you tell me if it is a dwarf hamster or a syrian hamster? (Is it larger or smaller than your hand?)
Dwarf hamsters (small ones) can be very cage aggressive if they live in too small of a cage. Cages sold in typical pet stores are mostly way too small for hamsters, unless you add on to them. So, if your ham has lived in too tiny of a home, it can become territorial and aggressively bite any "intruders."
For the future, get ready for bites when you go to pick him up. Start to notice his behavior RIGHT BEFORE he goes in for a bite. Learn these behaviors, and then learn to blow on his head, forcefully (although not TOO forcefully) so it distracts him from his immediate action: biting you. Keep blowing to keep him distracted.. he might either tire of it, or keep going. It's... not a science
But sometimes when you distract him by blowing on his head, you can scoop him up with the other hand.
Always always have treats on had to reward him. Never punish him (the blowing isn't a punishment, just a mild irritation), especially after biting you. Hamsters, like dogs, do not understand that they are being punished for a previous action. Instead, you have only the exact moment to correct a behavior.
If you need serious taming, then find a treat you know your hamster LOVES. Only give him this treat when you have successfully picked him up with out any bites. Again, like dogs, a delayed reward means nothing. You have to reward him for the good behavior RIGHT when it happens. This can be tricky. But overtime if done correctly, your hamster will stop biting you, because he will somehow know, if he lets you pick him up with no bites, he will get his favorite treat.
my research about mice says that they dont like things grabbing them from above because they assume they're predators and run... so hand taming, step by step is the best thing to do... my mice are nearly there, so when i need to clean the cage i pick them up so they can see my hand...