There comes a time in every man's life when he is up against immeasurable odds, and he must persevere toward victory through sheer refusal to face defeat. That time is most commonly referred to as "last call."
Last call presents many odds against a guy hooking up. By this time, there are usually no more than three decent looking girls at the bar that remain unclaimed. For some of those girls, last call is also a signal to end the night, so the "my girl likes to party all the time" vibe disappears quicker than Eddie Murphy's ability to choose a script. And most importantly, this is as drunk as these girls are going to be, so you may not be able to trick them into thinking you're attractive.
This is a time for the Hail Mary. Most guys have had one the 80-yard chuck into the end zone that somehow gets caught by the right receiver. It's a miracle pass that, when it actually works, surprises the guy who called the play.
The first strategy I recommend is the offer of the ride home. Before you try this, make sure you have a car with you or she'll get pretty pissed. If you're a big drinker, this is not a good idea nothing is less attractive than watching someone get detained by the police. This is much better than offering her a walk home, since she would only want to walk with a guy to protect her from sketchy guys like you. When you do drive her home, look for a parking spot before you get past her door. If you drive straight to her door, even if she invites you in, circling the block a few times kind of kills the mood.
Another tested strategy is the last minute cigarette. If you're not a smoker, I don't recommend you taking up the habit just for this, but I have seen the occasional last call woman that is worth a little bit of lung cancer. This works best in a place that has banned smoking, since you can bond over how much you hate the mayor/city councilman/your parents.
If you have a little more prep time, I'd recommend buying a ridiculous pet. I have met many guys who own bunny rabbits, but never one that likes bunny rabbits. If you want to get a girl you just met back to your place, you need an extremely compelling reason to get here there. The 4th season of MASH on DVD isn't going to do it, and neither is the thought of having sex with you, so get a rabbit.
And if you don't drive, smoke, or own an exotic animal, just be foreign. You don't have to be from another country just be exotic to your location. If you're on the east coast, be from Los Angeles. If you're on the west coast, be from New York. The important part is to talk about how the bars close MUCH later where you're from, and you need someone to guide you to an after party. You can even offer to host the party at your "friend's" place where you're staying. Besides, he's got a really cool rabbit she should see.