How to combine MirrorTexture and bump map?

There are a number of ways to ‘simulate’ the bump on a (water?) material.
May be have a look at this recent post using a node material:

Personally, I have also been using the ‘water material’ in combination with a ‘mirror material’ plane (before node materials) and got some good results. Obviously with animated ripples on the water surface, the ‘bump’ of a mirrored object doesn’t really matter anymore, because it’s overseen by the animated ripples on the water surface.