Yes, you can combine the bump map branch and normal map using Math.Add node or any other texture.
In fact everything connected to Bump slot of material is considered as black and white bump map.
To use normal map encoding of centileo bitmap (such as blue for unchanged normal and red/green gradients for normal vector changes) you have to check "Is Normal Map" flag in centileo bitmap. Then internally the normal map will be converted to black/white image ready to connect to the Bump map slot. And you will be able to combine it with other bump maps, adding, mixing, multiplying, etc.
Also keep in mind that converted bump maps (from normal maps) may have negative values in shader network internal opeations, because they show relative change of normal vector. These negative values are relative to unchanged normal and resolve for material correctly. But you have to consider this fact when for example you Color Correct them and probably want to apply some clamp for bumps.