The first four or five shaves is when you'll get the most blood. I believe it's because you're shaving down the high spots. It's kind of like a mechanical exfoliation for your skin. After the first couple of weeks you'll notice your face is smoother than ever before and you'll have stopped bleeding. I totally agree that you should enjoy yourself shaving as well as grooming in general. This is our righteous pursuit as the male of the species. Witness the preening of the peacock in order to create the best possible display for the ladies.

Oddly enough, keeping your razor well honed will give you surgical control over the blade and where it goes. If it's a bit dull, it will slip and cut you. Honing is not magic and you can learn to do it. Start by taking a razor and examining both sides of the blade from heel to toe using magnification. If there's a Radio Shack near you, they carry a handy Zippo lighter size illuminated microscope that gives you 60x - 100x magnification. It will really show you visually what's going on at the edge. Then lay the razor down on the stone and rub it the length of the stone so you can feel the metal abrading against the stone's slurry. Do about 20 strokes on both sides, wipe the blade clean and then examine under the microscope again. See what's changed. Keep doing that until you've got a clean, polished edge and bevel. Then strop on natural leather about 50 times. Then try shaving.