Say you are in a fixed reference frame. Bob, is in a moving reference frame. Also, Bob has a bar magnet. If Bob were moving toward you with a magnet, would the value of the magnetic field you measure be distorted in any way by the velocity? (non-relativistic question) Or would the magnetic field you measure simply be a function of your position relative to it?
Assuming that the magnet moving doesn't produce any emf (induced), the magnetic field won't have anything opposing it and then the field won't be distorted.
If the magnet produces emf, a current will most likely be induced. This current will set up its own $B$ which will oppose the original $B$, so the field will be distorted.
Check this out.