The place that should store up Dyes is the Glamour Dresser - accessible when changing up glamour plates. Need to get a few pots out to dye something you didnt store in there? Easy, just click the option to extract a number out.

Also to address a post above me, I think that the ability to make multiple characters per World extended to lowest-tier subscribers as well this year, but I'm not the surest of the intricacies since I don't subscribe but rather pay for game time.