Groom yourself better and get comfortable speaking with her. You don't have to propose marriage every single time you speak. Just talk and let your personality flow.
From what I'm reading, she's not interested in you. It could have to do with looks, personality, or both. But I'm not there so I can't be sure. Many times when eye contact is lacking between two people with potential, both are typically shying away from it. When eye contact is lacking between two people but one person isn't shy, then generally the other isn't interested.
Talk to her.you're coworkers so you have the perfect excuse.she's new also so you can be friendly and help her feel more welcomed.don't hit on her like you would at a club, just be casual and make conversation if you have things in common.treat her like you would any one else
Why don't you just be nice and friendly to her? Just say hi and introduce yourself. Don't be creepy or ask for her number or anything like that at least at first. It's really stupid to flirt at work with a co-worker you just met. But if you're friendly to her, she could warm up to you.
She hasn't expressed any interest in you and she doesn't even look at you in meetings. Unless she changes her outlook towards you and starts being friendlier, you should leave her alone if you value your job. Girls often have a hair trigger approach to claiming sexual harassment even if you did nothing wrong. There are plenty of hot girls that DON'T work at your office. Find one there, unless she makes it blatant down the road that she's into you. Even then, proceed with caution if you must.