Hey,
if your girl only takes 2 oz at a time, best to warm up only 2 oz initially. If she eats it really fast and seems hungry -- warm up a bit more, but the idea is that once the milk has been chilled, it loses its anti-microbial characteristics and you should not keep it at room temeperature for more than an hour. (In contrast, fresh milk has the ability of staying pure for several hours -- which means, if you are engorged at night, you can pump and leave the milk by the bed, while you go back to sleep).
In addition, once the baby has sucked on the nipple, saliva has gotten into the milk and has started contamination processes - hence, pediatricians recommend that you do not try to offer milk second time. Now, some lctation consultants say you can get away with it if you immediately chill and then warm up again and use soon -- but in this case it is simply easier and safer to be warming up small amounts at a time. Last, while you can taste a funly smell if the milk has gone sour in the fridge, you CAN NOT taste if it has been contaminated after it's been warmed up out of the fridge.