Ok, halley, it looks like you're right. Since we can "or" the bit sets, UnionFind is redundant in this case. UnionFind is meant for the case when one must build up the partitions from a list of edges alone. Since we don't know the edges and we have an easy set partition membership test, your algorithm is preferable.

I'm glad this was useful to break down your problem, even if it turned up a depressing word.