How to ask her?

Anon or delete. There is this girl at work (in a hospital) that I like. I started work last October and saw her then but we work in different areas and rarely see each other than the occasional time we are on the same ward or pass the corridor. This whole time I have tried to chat with her and get to know her but haven't been able to due to lack of confidence and lack of time I get to do so. I feel during the first month she definitely showed a liking towards me, but that could be her character as she seems outgoing and friendly. My problem is, I want to ask for her number or even to hang out, but I feel due to the lack of being around her long enough to have conversations (maybe had a couple short ones) and only occasionally greeting each other in the corridor, I think that even though we have known each other since October, we don't know each other that well and so asking would seem odd. Also, I have no confidence to do so whatsoever as I fear (stupidly) rejection. I know there are plenty of these sorts of threads and I am sure the typical answer would be "get confidence and ask" but it doesn't seem that easy and as I said, when could I ask if we barely have time to talk. I don't wanna walk past her in the hallway and stop her and ask.

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