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Your puppy is trying to get your attention. She associates the food bowl with getting attention from you (as you put down the bowl to feed her) so by bringing it to you, she is hoping for the same attention still. This attention can come by petting, love or from you giving more food.
Whatever you do, do not chase your puppy. By chasing your pup, you have started a game of which you will never win. She carries the food bowl, you chase her, she runs away creating a game of cat and mouse. Even if after a couple minutes you manage to get the bowl from her, she has already had several minutes of fun.
My advice to you would be to remove remove the food bowl after feeding time and ignore the attention seeking behavior