Maybe this is an artifact caused by excessive bump gain. Try to reduce the gain to, say, 0.01 and see if it still happens.

No that is not it although with 0.01 there is no bump and no problem.

I don't understand. You said that "that's not it" but you also say that with 0.01 there is no problem. So... did the problem disappear with 0.01 or not?

Yes.  But then I have no bump on the object.

Ok, so we know the reason: excessive bump gain, like I said.
I see two possible solutions:

a) increase the bump gain gradually until you start to see some bump but before you start to see that strange effect.
b) use displacement (tick the "displacement mapping" checkbox).

Alright I will try both tomorrow.

Another thing which could be important:

I noticed you have black and white for your bump map. Don't forget that in Vue black is down and white is up. So, you're raising the white parts and lowering everything else. Is that what you really want? I would suggest that you use gray (127,127,127) instead of black. Gray is neutral.

Ahhh... That sounds like the problem, I'll try that. Thanks.