A sharp bump map won't prevent self shadowing if the bias is too low. In fact it may make it worse.

But you even get the artifacts with shadows switched off? Hmmm.....

What about the geometry of the object? How about ticking Remove backfacing polys in the render settings? Make any difference?

"If I were a shadow, I know I wouldn't like to be half of what I should be."
Mr Otsuka, the old black tomcat in Kafka on the Shore (Haruki Murakami)