Riccardo,
I'd say Magnum is on point, although I wouldn't use any of the 3 approaches you've listed. If this Bartender is Hot, virtually nothing you say is going to differentiate you from every other guy who's tried to pick her up.
I worked in Food & Beverage and Nightclub Industry in Las Vegas where all the female bartenders are hired as "Models" and are paid to look good. If you aren't industry, or ultra high status, the most effective way to pull a bartender while she's on the clock is to:
1. Frequent the bar enough to build a unique rapport with her that's based primarily on your Social Status and familiarity with other industry workers that she's associated with.
2. Start by ordering your drinks specifically from her - be particular about how you like your drinks made. Do not chat her up beyond your normal please's and thank you's.
3. Tip Her WELL the first handful of visits. I call this a "friendship deposit". Bartenders love generous clients and they'll remember your face. If she's cool she'll eventually start pouring you free shots and the like in return for taking good care of her. This makes you good in front of the other bar patrons. Pay with Cash.
4. You've been to her bar 3 - 6 times, you've already added half of the other bar staff on Facebook because you've been there enough times to create some social status. This is when you begin to chat her up briefly and casually. You finally get her name (even if you already know it), you make it an official introduction. You talk shop, if it goes well, you get her Facebook.
5. Weather through Facebook or otherwise, She's now going to realize you have some mutual friends, some status, some pre-selection. This is the key. After this point you can go ahead and game her because she's less likely to see you through the customer service lens. And more likely to consider you as an option.
See where this is going? Of course there are exceptions! You may be an exceptionally charismatic, charming-asshole and may only need to visit her a couple times, bust her balls, get her number and skip the whole process. But generally these are the necessary steps to pull the sexiest, most badass bartenders.