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I know that normal mapping describes the process of adding detail to meshes without increasing the polygon count, and that this is achieved by using specific normal textures for manipulating the way light is applied to the object. Okay.
Bump Mapping describes a general technique for simulating bumps and wrinkles on the surface of an object. This is normally accomplished by manipulating surface normals when doing lighting calculations.
Normal Mapping is a variation of Bump Mapping in which the surface normals are provided via a texture, with normals embedded into the RGB channels of the image.
Other techniques, such as Parallax Mapping, are also Bump Mapping techniques because they distort the surface normals.
To answer the second part of the question, they could fairly easily be combined. The base surface normals could be determined from a normal mapping and then modified via another bump mapping technique.