You can engage too fast in having a connected conversation with a girl.
The key is to first exude confidence and power.
If you try and retreat within the comfort of a one to one connection with her and you do that too fast, you don't give her the opportunity to see you "from the distance".
This oveall view she gest from you first is what triggers sexual attraction.
Building comfort with her comes after.
First, you need to express the signs that let her see that you are a sexually attractive guy.
Start first by being centered, own your space, express your social connection to the room.
Don't over focus your attention on her or you will appear that you are looking for a way to exit the overall social sphere.
If you enter the room and go straight to her, you might rob her from the possibility to see your "role" within this social context.
Imagine instead that she sees you interacting with women, she sees you connecting with friends, she reads confidence in your body language, she sees total emotional power in your smile.
All these trigger the first levels of sexual attraction towards you.
Once this first degree of connection is established, you can go to the next stage and start building emotional intimacy with her.
That's the comfort building stage where she realizes you are a safe guy and she can relax in your presence.