If I ask her to somewhere, I believe that I pay for the whole thing. If she suggests somewhere, she is paying unless she asks me to pay.
Asking her to go half should be something done after you have already established a relationship with her, and should be used in strategically.
Me and my lady regularly buy rounds, take turns paying for date night, etc. you just can't try to use that shyt for leverage. That's when you become a scumbag.
If she ain't worth impressing, why the fukk are you breaking bread with her? You could easily do something cheaper and still get sex.