Most men don't know how to lay the groundwork. They imagine that just maybe a girl likes them and then they pop a question awkwardly out of the blue. They freak out because all of a sudden, in an instant, the little flirty game they've been playing become real.
You should have softened the target beforehand. That involves engaging in small-talk, ever so slowly transitioning to more personal subjects and feelings. Yes, feelings. After that comes gradually "musing" about life. Show yourself as a thinker and philosopher if you have the ability. This separates you from the rest of men, because women perceive men as shallow.
Once that is done, the man should be on the lookout for an open invitation from the woman. This will take the form of lots of direct eye contact punctuated with looking down in submission, a very definite smile and an eager happiness when you walk into the room. Once you see these things, the work is already done and it's almost a sure thing.
Don't ask for her number abruptly. Instead, find a day date you plan to attend and casually mention it in a conversation if possible. Say, "Hey, why don't you come with me?"
NEVER suggest being friends. That reeks of insecurity and dishonesty. A woman wants a man who is bold and direct and takes what he wants. Never hide behind "Let's be friends". She will always see you as a friend in that case. She will not be able to shift.
Finally, let me say this: I had the experience once of playing with two baby lions and getting my picture taken with them. It was the last day the trainers were able to do this because the lions were getting to big and unwieldy. I thought how cool it would be to have a pet lion. But there is a reason we don't keep pet lions in the house even when they are raised from infancy. This is because they are slaves to their instinct. They can be friendly for years and years as adults if you've raised them from birth, but one trigger can cause them to kill you. Again I say they are slaves to their instinct.
In like manner, if you go out with a coworker and things go bad, she WILL be triggered to tank your career. She won't even know she's doing it, but she will say the most bizarre things to management that will implicate you in something or another. I'm convinced they do this completely subconsciously, but the vast majority will in fact do this.
Don't dip your pen in the company inkwell unless she works in another building.