the first part of the story
“I’m doing this because you’re a good cop and you’re pretty, and because you’ve never cared that I’m as ugly as an old tire. None of that means I’m willing to lose my job getting you in to see this son of a bitch. Are we clear on that?” She nodded, mouth tight. “Good girl,” he said, and offered the only smile she was liable to see. “Tight on my six; humble fucking pie.”
What does " offered the only smile she was liable to see" mean?
What does "Tight on my six; humble fucking pie" mean?

Question

the first part of the story
“I’m doing this because you’re a good cop and you’re pretty, and because you’ve never cared that I’m as ugly as an old tire. None of that means I’m willing to lose my job getting you in to see this son of a bitch. Are we clear on that?” She nodded, mouth tight. “Good girl,” he said, and offered the only smile she was liable to see. “Tight on my six; humble fucking pie.” 
What does " offered the only smile she was liable to see" mean? 
What does "Tight on my six; humble fucking pie" mean?

Answer

1: Gave her one smile. She was unlikely to get another from him. 
2a: Stay close behind me.
2b: I don't know. I guess maybe it means to not be a hero?