You want washers, nuts, and bolts. Screws may strip out at high speed. Some folks have mentioned the splitter buffeting in the wind at 70MPH+ cruising speeds. However, just a quick wrench turn to tighten the bolts/nuts fixed their problems. With screws, it won't be tight, and will flap around for sure - then it may rip out, and you'll have a busted bumper cover on your hands. Just get the right hardware the first go-round.
Mine's been on the car for 2K-3K miles now. It has seen a few 80MPH+ cruises and sprints, never even got a shudder out of the splitter. Great product, easy-as-pie instructions, and the hardware kit even comes with an extra 1-2 of everything (well, mine did). Spencer's a great guy with great products. Won't hesitate to buy from him again.