Shango used to do that, but I have mostly put a stop to it now. He would jump up and bite at me (usually breaking the skin a little bit). Definitely don't tolerate or enforce this behavior or it will only get worse. Most of the time I could just grab whatever toy was close by and kind of use it like a shield to block myself. Then once he'd start "attacking" the toy, I'd tell him good boy. When he was going after me, I'd tell him a very firm no and would also say loudly ouch that hurts mommy (whether it hurt or not). If the toy didn't work, I'd leave the room and close the door behind me. Then once he had some time to calm down, I would go back into the room.
When he was younger, I had the most problems in the middle of the night/very early morning when I was trying to sleep even though I always have a long play session with him before bedtime then feed him. While I was sleeping, he would all of a sudden pounce on me. Then he'd bite me wherever he landed at... face/neck area which was rather scary, arms, legs, didn't matter. Usually it was not hard enough to break skin, it was more of a pinch. Of course the pounce/bite would always wake me right up and when I'd pull away sometimes his teeth would scratch me so it looked like scratch marks instead of bite marks. I started sleeping with a squirt bottle under one of my pillows. Whenever he'd pounce on me in the middle of the night, I'd tell him no and squirt him with it and most of the time he took off running and would then leave me alone. I would then hear him running around playing with a toy or on his cat wheel. There were a handful of times when he just wouldn't give up... I'd have a dripping wet cat with a wild hair up his butt intent on pouncing on me. Usually at that point I was so irritated and tired I just gave up and would close the bedroom door. Depending on where he'd run to, I would sleep in the room without him or a couple of times I ended up sleeping on the couch while he played in the room. It's a huge difference having a 4 lb kitten pounce on you vs a 15 lb cat so you definitely want to put a stop to the behavior sooner rather than later.
The pouncing/biting in the middle of the night has now completely stopped, but Shango still occasionally gets nippy with play aggression. If distracting with a toy doesn't work, I leave the room. Then when I come back into the room, I'm greeted by him rubbing up against my legs and giving headbutts... almost like he's trying to say he's sorry.
Savannah's are smart so be consistent and patient and things will get better.