DC bias is a constant DC signal that is superimposed onto one line.
Common mode voltage is a common signal that is being superimposed onto two or more lines. You can have a common mode voltage that is a DC bias, but the common mode voltage does not necessarily have to be a constant DC (EMI-induced noise for example).
So basically, common mode implies something that is shared between two or more lines. DC bias is self explanatory and doesn't imply sharing between lines.