I don't know why we're all supposed to pretend that the children who are injuring others and telling other children they'll come kill their parents in the night aren't going to grow up into psychopathic abusers. The person I knew in grade school who was like this, and similarly excused by his mother, grew up to go to prison for murdering his ex-girlfriend
Oh hang on a minute, we don’t have to discuss it any more and can, in fact, have a huge impact on future offending rates because @WombOfOnesOwn ‘knows someone’. 
OP ignore the people here writing off Bob and creating additional dramas.
Report every incident to the school Principal in writing.
In the letter, state that you expect action to be taken or you will escalate the issue due to safeguarding concerns.
If / when no action is taken, write to the chair of governors.
If / when no action is taken write to Ofsted.
If / when no action is taken report to safeguarding.
Don’t mess about waiting between each stage, another incident another letter and the next stage of action.
BUT
Don’t go to Bob’s mum. Whether she is trying to address this issue or not, it’s not having an effect.
Don’t slag off kids who may have very challenging problems and may not be getting the support that they need.
Don’t expect to be told what they’re doing or what’s going on with Bob because they can’t tell you. But ask for details of how your child will be protected.
Don’t believe the nonsense that you’ve read on here demonising kids because someone knew someone at school.
If you approach it in a measured way Bob will end up getting the support that he needs because school will have no choice but to provide it and as a result your daughter will be safer.