I am also torn between referring to interpersonal.SE and answering here, but there are some gaming-specific aspects, so I'll answer here.
(And please understand I'm writing this answer not just to you personally, but to a future audience of everyone who sees the the question and reads this answer.)
1) Be a gentleperson from start to finish
...whether the finish is in five minutes or fifty years. This is the same advice you'd get for any relationship: Don't be a creep, don't be a stalker, don't refuse to take no for an answer, etc.
2) Dating and gaming does not inevitably lead to bad outcomes
I've gamed with spousal pairs as players, I've gamed with spousal pairs as the GMs, I've gamed with couples dating through games, I've introduced a girlfriend to gaming, I've seen others do the same for their significant others, etc. I cannot specifically recall a GM asking a player out for the first time during the tenure of a game, but I'm surprised by that fact.
The overwhelming majority of these situations, including mine, have been positive, at least from my vantage point. And while horror stories abound, the worst I have ever personally experienced have been fairly mild. ("Really, buddy? +5 Holy Avenger for the third level paladin?")
3) But your concerns are real and they are valid
Because the thing is, there is a power imbalance between a GM and a player. It's not a huge thing in the context of the real world, because it is a game. But it is a potentially huge thing in the context of a game because one of your is in charge and the other one isn't.
This means two things, to my mind:
First, see 1) above: Be a gentleperson. That means taking extreme pains not to link the date (or the request) to the game in any way.
Second, I won't lie: If she says yes and you end up a couple, this can be a source of stress as you struggle to maintain fairness in the game without over-reacting, and also keep a healthy and happy relationship. But I can assure you it is not insurmountable.
And maybe one day, you two will be one of those adorable spousal-pair GMs!