This color bleeding sometimes happens to me too, but usually when I rush putting on the details - not letting the base icing dry long enough. You said you waited overnight, though, which is strange 'cause your base icing should have been fairly dry.
Maybe the icing you used for the dots was too runny?
One little trick I've found is to use a fan, goose-neck lamp or a slightly warm oven (DO NOT LEAVE IT ON, though) to help dry the icing faster, before it starts to run. Seems to work for me. It also makes the icing dry slightly shiny.
The one thing I haven't quite figured out is how to pour two colors at the same time and then drag a toothpick through - to get that feathered look. One color always seems to bleed into the other eventually. I'm going to try my oven trick, though, next time I make these, and see if that helps.
There was a thread recently on drying royal icing - maybe that will help you.