You can abuse the Minecraft spawning physics to make a spider spawner. You see, all other hostile mobs (except maybe slimes, which only spawn at the bottom of the map anyway) require a 2 blocks high space to spawn in. However, spiders require a slightly different shape, a 3x3 square, but only one block high. So, if you want to spawn spiders, your best bet would be to make a two squares, one on top of the other, with a block of empty space between them. Due to the low height, only spiders will be able to spawn on the lower square, and because of the darkness (if you wall off the edges or make it large), they'll be the only ones to spawn there. You can then remove pieces of the top (when it's light out, so they'll be non-agressive), kill the spiders, and collect the string. (Obviously this would be impractical if you needed to reuse the device often, but since string is only really needed for bows/fishing rods, you don't need more than a handful of spiders)