Is magnetic hysteresis present even with a DC bias?
By adding a DC bias, you are just shifting the hysteresis loop to another operating point. You are not eliminating it. The smaller the AC component of the  current, the smaller the hysteresis loop and the related non-linear effects of the core.
The linear relationship of \$B = \mu H\$ is only an approximation in this case.

Source: Magnetic Hysteresis