1. A small, single-serving pizza, most often between eight to ten inches in diameter and with a thin crust, which is purchased and eaten at a tavern, bar, or other establishment which typically sells more liquor than food.
2. Any small pizza-like foodstuff ordered and eaten at a bar. Though some places make their bar pies to order and serve them fresh from the oven, at many lower-class joints a little frozen pizza is simply thrown into the microwave. In these cases, though, the poor quality and lack of any resemblance to a "real" pizza is often overlooked due to the typically intoxicated state of the consumer.
Nah, I'm not hungry -- I had a couple of beers and a bar pie over at Smitty's.