You don't have to "chase her just to find out if she will slap a restraining order on" you ... you're taking things way further than I intended. If she's to that point, you're well beyond a determined suitor and into stalking territory. Don't go there; just move on.
But, as to jumping through hoops to win a woman's heart, including the "hoop" of facing down your own fear of rejection by maybe not taking a "just friends" putdown at face value ... yes, you will need to do that, so get used to it.
The "bridal test" theme -- the brave deeds the hero has to do to win the girl's heart -- is found all over literature. In fact, arguably, Christianity is a whole religion whose central theme is the hero (Jesus) suffering the bridal test (the Cross) to win his Bride (the Church).
I don't know much great literature off the top of my head, but I can give you three examples from the world of opera: Wagner's Meistersinger (the whole theme of the opera is a bridal test); Wagner's Ring of the Nibelung (two separate bridal tests for two couples in act I of Walkure and act III of Siegfried); and Puccini's Turandot (again, the bridal test is the whole theme of the opera, only this bride isn't just reluctant, she's positively deadly -- but finally folds under the relentless ardor of the hero).
Why is this literary motif so common? Because it's true! It's true at a level that's almost subconscious, sure, and some women (often liberal ones who are trying to deny their own nature) will deny it, but it's still true.
Look at what the women on this thread have already said. They admire Braveheart, not Caspar Milquetoast. You don't have to have 16-inch biceps or moviestar looks, you just have to show them you have the heart of a hero.
I don't care as much for Wagner (modern attention span does me in, I guess...), but Calaf is AWESOME! No wonder she finally give in!
Not to take this thread into a whole new direction and off topic...oops!
Another example is Mozart's Die Zauberflote...which I liked enough to name my cat after the prince.
I'm odd. Fun, too, I'd like to think...but odd. ;-)
Well, I'd like to deny it... I don't think there are many women who have their plan together well enough to put up hoops for a guy to jump through to for the sake of making a guy pass some heroic test. Not women who have reached the age of maturity.
That isn't to say that resistant hearts can't be won, sometimes they can... but I wouldn't get into the trap of thinking women, or men, have it all figured out and are playing a game for which only they know the rules, most of us are just doing the best we can do find and be good mates.