Yes, you can use the pumping machine and feed her with bottle. From what I have known, it is good to use the pump right after you BF to clear the leftover milk (if there is any), and this method can help increase your milk supply.
For the bottle-fed, it depends on how and what you feed your baby girl. If the position is right, you burb her afterward, and with time for her digestive system to mature, the problems can be less. Just don't forget to use the natural bottle teat to mimic your breast.
Hope it helps :)