Some people say the other way gives better quality, but it certainly works to dry them on a screen. How quickly they dry probably has more to do with quality than anything - don't pile them higher than an inch or 2 and check on them constantly. Bud molds very easy.
A tiered drying net makes harvesting easier and gives you a ton of surface area to dry your bud on. If you get a hanging scale, you can weight the whole net, which is nice.