I am trying to create a street scene, and I am using an image texture and a bump map which is connected to a noise texture. However, the rendered result looks nothing like the material preview.
Try using texture coordinate/object into the noise node and adjust noise scale and bump settings accordingly. Preview is not a very accurate thing - it can show you what effects are involved, but you have to take care of proper scaling to your object yourself. Preview doesn’t know if you’re modelling earth or a marble. If on 2.80, I’d use the shading tab as a replacement, even if it doesn’t show everything Cycles specific.