The Celts (and presumably other cultures) could make bright dyes. They would mix them with whatever was locally available, white powders, egg yoke, etc., to lighten them, and things like copper to darken them to certain hues, mixing things until the look they wanted. The dark age and medieval Irish and Welsh still used a lot of bright colors in their clothing, because they had available dyes for it; Irish burial cloaks from earlier periods contained bright colors (particularly bright blue, yellow, and red). The Dal Riatans and earlier Caledonians though lacked such dyes. One example of a simple dye that's somewhat bright is woad. Woad is always depicted as blue, but if you soak fabric in it, it will have a bright purple-ish color (not really purple, but similar). That was a common dye, and very much more common during the dark and middle ages.