Mo Ling was already mentally prepared to confess her identity if he ever asked so she didn't avoid him when Snow hesitated to speak.
First she trusts him. Trusts his character. She trusts that he won't hurt her. She didn't know when this deep trust began towards him. But she didn't want to think deeply about it.
Second, even if he listens and wants to interfere in her matters she wouldn't let him.
When Bi Yuhan saw the look in Snow's eyes he knew that he needed to leave them alone.
After all, the boy has his own secrets which might be fatal to his life when uncovered.
He didn't want to take that chance towards the boy's life.
So he got prepared to stand and leave the room when he heard the kid's words and got stunned.
Then the next second happiness bloomed within, his lips curled up unknowingly to form a faint smile which reached his eyes.
'The boy trusts him. That's more than enough for him right now.'
After making up his mind he didn't leave.