Brest milk in the bottle??

Little back ground: I'm a first time mom. My little guy is 5 days old and I have chosen to breast feed. My milk came in on day 3 and I feel like I produce so much milk. I can feed my little man for about 20 minutes, but after I can still pump out almost 4-5oz of milk. When i go to feed him before I can get my nipple in his mouth my milk dripping all over his face, all over me. While he is on one nipple the other nipple is dripping everywhere. If I leave the house after I have fed and pumped my shirt is soaked in less than two hours. I've been considering just pumping my milk and giving him the bottle. It's so much easier and he seems so much happier on the bottle. I still have offered my nipple and he takes it just fine. Any suggestions? Do you guys think there is anything wrong with bottle feeding breast milk?