TwiceAsNice, it's normal to be scared, I was, I've had 3 GA now and am much less nervous. Remember, anaesthetists are considered to be the brightest of doctors, the best trained and I have found lately, the friendliest.
They are there to look after you. Your safety and well-being is their only concern.
In my last operation, a robotic, keyhole hysterectomy, the anaesthetist and surgeon both chatted to me immediately before the operation. I could chose from his playlist what song I wanted to 'drift off' to. I had the operation in Holland, so, as I am a Brit, he suggested The Beetles' and he chose 'Yesterday'!
If you think of the words, it shows he had a sense of humour!
Good Luck!