I know this topic is 21 days old at least. but i just registered and it was still on the first page so I'l share some tips anyway.
The best way to get white wool without having to run around hitting sheep all day. (RL-day that is) is to farm spiders from a spider spawner. 9 spider thread = 1 wool block.
getting the color is the easy part imho. but ofc. while out gathering color materials it pays to color any sheep you do come across. but the spider spawner is the main thing. even a gigantic darkroom trap can net you quite a bit of spider thread if you cant find a spider spawner anywhere to supply you.
One spider spawner trap can easily net you 4 or 5 stacks of wool in a couple of hours. just place yourself in the collection pit and go eat dinner, go to work or whatever you do when not playing minecraft.
