Dirt can be made in say Gimp or Photoshop. It can be a UV layer added with a blend and adjusting with the FAC. So if you have a diffuse color making that color and want to add a bit of grunge to it. Send that diffused baked layer over to P.S or Gimp create a new layer on top and add to taste. Then assign it as the color or material. So you could make a square of the color desired, send it over to PS or Gimp, lay a grunge layer over the top. Make half of the layer grungier with (variety) so when UV unwrap and assign you can move it around your layer to select what part is dirtier then another. Think Gradient.
Or you could make a layer by itself with alpha PNG export and mix blend on top of what you already have.
You will not have bump map for it doing it that way… However, if you made separate layers as mentioned in PS or Gimp and then assigned it to a puckered or lifted geometry face. You would get dirt, 3d too. Or make a bump map, spec map and color map.
I am new to Blender and learning myself, however this is something I am dealing with right now. There are many ways to do Art in Blender, I am sure someone may have another way to proceed.