After a long nap, Bai Jingfei was up and ready to go figure out what contest heavenly doctor Ming had made her jump through all these hoops for.
She had initially woken up extremely confused about where she was, and ready to scream out of fear, but when she saw Song Yongrui's face right across hers, she somewhat calmed down. If he was there she probably hadn't been kidnapped.
Song Yongrui was sleeping peacefully, but pretty much the second when Bai Jingfei woke up, he woke up too. It was probably because Bai Jingfei was moving around when she woke up.
It wasn't like Song Yongrui was a heavy sleeper. He was the lightest of the light sleepers. The slightest noise could snap him out of a daze, let alone all the noise from Bai Jingfei moving around. Even her slightest movements would wake him up.