Does this girl like me?

Either your time might be completely off, or you both don't want to be pushy, or she is just leading you on. You are not pushy. If you want to get to know someone, you have to ask them out, either as friends or more, but without spending time together, you will always be just coworkers. Don't worry. Do an experiment. Just ignore her for a while, get a little distant, act like you have a life and you don't really need anyone. Since she has more guy friends, means she is not the shy type around guys. See whether she cares enough to get closer to you.