Thank you, eventerdrew!
OK, just an update... (no good news though
I tried different bridle with different bit yesterday. It was one-ear western bridle. The bit was Korsteel eggbutt french link. Same shaking, plus she looked pretty unpleased with this bit. And she shakes the head when I'm on ground, not on saddle, as well as saddle wasn't even tight. I also noticed when I was walking her in just a halter, she throw her head and mane too exactly the same way. So to me it looks like that strap going behind the ears somehow bothers her. The only time she doesn't care is when she is grazing. Lol! I have no idea what can be done else. May be shave her mane down there. But I kinda afraid to spoil her look. :)