Not exactly.
It doesn't have to do with bias so much as how we slice and dice what we observe (which could be biased). I say a coin has heads or tails…
Not exactly. A universe is really a set of observations that you or I make about reality. In quantum many worlds, we believe that each possible observation of a quantum experiment, which as random outcomes, have their own universe. So, if I flip a (quantum) coin, there is a heads universe and a tails universe. Each one has a copy of me in it, one of me observing heads, the other observing tails.
It doesn't have to do with bias so much as how we slice and dice what we observe (which could be biased). I say a coin has heads or tails but that is an interpretation of that coin that I have made. Even if other people agree with me, the coin doesn't know that it has heads or tails. Therefore, there cannot be a heads universe and a tails universe.