​Scrub radius and bump steer

Bump steer is the result of the configuration of the lengths and/or angles of your steering and suspension assemblies which cause the wheel to turn throughout the suspension travel. It's a separate topic from scrub radius or Ackerman. Bad bump steer properties can make Ackerman worse or at the very least inconsistent.

You want the outboard of end your steering arms and suspension arm ends to describe the same arc (or as close to it as possible) during full suspension travel.

In direct response to your question, wheels, spacers or wheel offsets won't have any impact on bump steer.

I have a Datsun 240Z that is very prone to bump steer if the stock suspension is lowered. On the inner end the steering arm is about 4" higher than the inner suspension arm pivot. They are nearly in a horizontal plane on the outboard end. As the suspension move through it's travel the outboard ends of the steering arm and the suspension arm are describing different curves and creating steering input.

On the Datsun the (sort of) solution is to put a spacer on the bottom of the strut to which the suspension control arm attaches to try to make he control arm more parallel with the steering arm. Another option is the raise the inner pivot point of your control arm to the same effect.