How does inserting a shunt in the brain not cause bleeding or damage

It can: But in the well trained hands of a neurosurgeon, he/she should be able to minimize the risk of either. They utilize techniques that minimize trauma to the brain and it's vascular supply .... that's why their training is soo long.

Location, location.: A shunt is situated in a fluid-filled cavity within the brain. No blood, and no structures to damage. The surgeons are adept at placing them just right.