So, this is the situation - input bias currents flow through the input voltage sources and their internal resistances. If there are additional resistors in series (as in the case), bias currents will flow through them as well. You can see this in the simplest differential pair (in principle, this is the same configuration). Let's first consider the case with equal input voltage sources but with no base resistors included (Fig. 1):
As a result, bias currents "create", according to Ohm's law V = I.R, voltage drops across resistors. They are constant since both current and resistance are constant. So, we can think of this resistors as of "batteries" with constant voltage that are connected in series to the varying input voltages. Depending on the polarity, these voltages will be added or subtracted to/from the input voltages; thus they "shift" the varying input voltages with some small constant value.
Let's, for example, now consider the case whenwith zero input voltages but - one of them "ideal" and the other real. For example, the left input (T1 base) is directly grounded and the right input (T2 base) is grounded through a resistor RB: