Should i ask this girl out?

Theres this relativley new girl at work who is real nice looking and looks like she would be a gem to get in a relationship with.. problem is i dont know if she likes me or not/single? when we've ped each other in the corridoors shes looked at me and smiled.. not stared at me. I dont know if im just being too desperate on my side to thinking i have a chance or should ask her out. I cant tell if shes single though because of the way she dresses (respectivley/casually) as your not going to get away dressing like a tart.. although she dosnt look like that type anyway. We havnt talked yet simply because we are in totally different dipartments.. i do maitenence work whilst shes in the offices so ive never really had a chance to talk to her. How would i find out shes single/likes me? is it wierd to sit down with her near the end of the day when most of the offices are empty + hers and ask her then or leave her my number when ive hardley spoke to her.. im quite shy too but im willing to break the barrier to get to know her better.. whats the best way to go about this.. any ideas?