Bones wasn't afraid of him. Just the situation itself. The fact that she might never wake up. Or that she was really here, and had simply been plucked from her life. And his explanation about The City scared her. In Bones' world, she could control almost everything. And from what she was beginning to gather from Sweeny, that was absolutely not the case here.
She bit down on her lower lip, commanding herself, because her own self was probably the only thing she had left to control, not to cry. And she didn't. She managed to swallow the lump in her throat. She even managed to reply. "I... but how did I get here?" She couldn't explain it, and no matter how many scenarios she went over in her mind, none of them seemed to add up.
She realized then, that she had been rude. She had been having a sort of conversation with the fellow and didn't even know his name. "I'm Dr. Temperance Brennan, by the way." She wasn't sure she wanted to shake his hand, but she held hers out anyway. Maybe touching something solid, or someone for that matter, would seal things for her. Make her believe it, finally.
"No, you don't frighten me." She chuckled slightly, dismissively. "It's all just a little overwhelming, isn't it?" She was going to accept it. She might come to find out later that it was one big ridiculous dream, but she didn't seem to be waking up and it seemed the only logical choice. Falling apart and refusing to believe she was where she was would really get her nowhere.