ysth,
I haven't spent a lot of time analyzing the distribution frequency, but this implementation does have the possibility of clumping as both you and bart indicate. This, however, is only one of dozens of variations I tried over the last couple of days and others were better at being more statistically uniform.

I was hoping someone else would give it a try to see what they could come up with as there are far smarter monks here than myself. I know it seems silly. The answer without restrictions is obvious, assign to an array and shuffle. It just seems to be that there should be more efficient ways to reduce the search space, determine an unchosen bit randomly without a lot of work cycles, etc. It is obvious to me I need to learn more about bitstrings and bitwise operators in general.