Okay so here's my conundrum. I've been stuck on it for a month or two at this point and need advice:

There is a really cute girl at work. Problem is she doesn't work in my department, and I would never have a work related excuse get chatting to her. The only time I see her would be in the canteen or walking down a corridor. The vast majority of the time I see her she is with her colleagues, and I'm with mine. There are so many people at my workplace that sitting down beside her in the canteen isn't an option, it's always packed during break times.

Any time we make eye contact though she says hello and gives this shy little smile so I'm pretty sure she likes me too. Here's a catch though - I vaguely know one or two of her (male) colleagues, and have learned from one of them that she has a boyfriend (90% sure she has a boyfriend). I don't know her colleagues well enough to fish for any more information or for any hints as to where she socialises so meeting her out some night would be pure luck.

What is my best strategy for getting to talk to this girl? Am I actually going to have to stop her in the corridor and start talking? If so, what the hell can I say to her knowing that (a) she likely has a boyfriend, and (b) the corridor in work isn't exactly a prime location to lay some groundwork with a girl? What should be my opener?

Any advice is greatly appreciated...

Don't be so concerned about what you open with. If she is remotly interested in you (which she seems to be), almost anything will do.

If you just needed to know a line to pack up the ballz to go talk to her I'll give you one. It's a variation of strimpboi's supermarket opener. It will work best if you see her 2-3 times a day (you can always arrange it)):

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You: "I need your opinion. I've seen this girl at work a few times, she's kind of cute and she smiled at me, my question is, were at work, are women really open to starting a conversation at work?"
Her: Yes/laugh/whatever
You "Really? So I should just say hi and introduce myself to her?"
Her: Yes/whatever
You "Cool, thanks" and I walk off.

Next time you meet her:

You "Hi, I'm revolutionary. I got some great advice to just come up and introduce myself to you"
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If you don't like the time it takes between the two encounters... you can always go with one of my favorite from David DeAngelo:
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You: Hey, I have a quick question for you. *pause and look suspicious*
Her: Sure
You: Are you single?
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Alright you have a line. Now go talk to her!