Total voltage error at the output of the Op-Amp
When attempting to calculate total output offset you must consider the effects of Vio and Ibias separately as you are trying to do. To calculate the output offset due to Ibias let's assume that Vio (input offset) is zero and that the input bias currents are equal to each other (Ios = 0). Let's also name the input signal source resistance as Rs.
If Rs is equal to zero Ohms (ideal voltage source) then the offset at the output due to bias currents is equal to Ibias*R1. (the bias current from the non-inverting input flows straight to ground).
If we were to now slowly increase Rs then the output offset would linearly reduce with increasing Rs until the output offset due to bias currents equals zero volts when (Rs//R3)=(R1//R2).
Note that Vio can be positive  or negative causing either a positive or negative output offset. Similarly the output offset due to bias currents can be either positive or negative, depending on whether the op amp's input transistors are npn or pnp. This means that the output offset due to Vio and the output offset due to Ibias can add together or partially cancel each other out.