@Sir Sam Vimes,
What should you do?
Say something like this.
"A, let's go out to dinner on Saturday night. Are you free?"
And she says either yes or no. If she says no, ask about Friday or Sunday or whatever. If you get three No's, forget it. If you don't, then it's just a scheduling issue (by the way, the three number is fluid; just gauge it by interest, enthusiasm, or lack thereof).
When you get to yes, say,
"I want this to be a date. I really like you."
She says something like this.
a)
I'd love to. I was hoping you'd make a move.
or
b)
I'm sorry. I really just want to be friends. I hope I didn't lead you on.
Note – get agreement on the dinner before telling her you'd like for it to be a date. This is not bait and switch. Rather, it is giving her (and you) a more gracious exit if she gives you three No's and it's clear that she isn't interested. But you do need to say that second piece, about wanting it to be a date, as not everyone can pick up subtle signals.
In short,
(1) You ask to spend time together. Friends spend time together.
However, you are asking for dinner on an obvious date night, so that should be a clue to her. If her answer is going to be (b), she's already clued in that something is up and, if she is not interested, she may make the (b) speech then.
(2) You persist if the response is negative, but only a little bit. You attempt to be accommodating if it's truly just a scheduling conflict, but you back off if you're getting roadblocks. You don't overdo it. You don't go all stalker-y.
(3) If an agreement is reached, you make it clear that you want it to be a date. You also make it clear that you really like her (if there is any interest at all, she will love hearing that. If she's been with a lot of jerks, then it's likely that many of them didn't tell her that, or didn't tell her that too often).
(4) You are giving her the opportunity to back out if she was uninterested in you that way and not clued in by the time you got to the third step.
Oh, and
(5) If she says (b), then be gracious and say that you're sorry you bothered her and let that be the end of it.
Warning: you may lose her as a friend, despite how kind you've been. That happens; people feel awkward. But you'll be able to hold your head high and will also be out of the friend zone rut of wanting but not doing. And if she says yes, well, make it a nice dinner but don't lay a million expectations on it. It's dinner with a lovely date. Wait until at least your third date to start discussing china patterns and baby names.
PS I can practically guarantee that at least one person will tell you to treat her like dirt and that that will get you an in with her. If I were her, I'd be appalled, and angry at such treatment from someone considered to be a friend. You may strike out with her but you say you've got a boatload of female friends. If you start acting like a dick, they will notice and, if it doesn't happen with this girl, you may find you've poisoned the well with all of them. So be aware that, like it or not, there's a bit of an audience. You don't need to play to them, but do be aware that if you're a Grade A asshole, she will likely tell her pals.