I’m using a Bump map with a resolution of 4096 * 4096, but whether it’s preview or final rendering, there’s a rugged mosaic on the surface.
The way Blender displays bump maps is really, really shitty, even in 2.80.
There are two issues here: The visible steps in bump depth, and the oversized bump pixels.
You are most likely not going to see those depth steps in any game engine (if that’s what this is for) because they always add a certain amount of blur. However, if this model is going to stay in Blender, you won’t be able to get rid of these artifacts. Redoing the texture at a higher image bit depth might help if you’re not already at “32bit float”.
The pixelation comes from the fact that Blender’s viewport renders bump maps at half screen resolution. The actual resolution of your texture has no influence on this and is unrelated to the issue. Bump map pixels on the screen are always going to be rendered twice as big as everything else. (They’ll be shown at regular size only if you render the image.)