The definition of bullying that our children were taught was something like repeated unwelcome actions.
Repeated is key. One of fight/incident etc isn't bullying, repeated is.
The teacher in your case is very out of order. School incidents must be dealt with at school. To suggest you go and talk to the other parent is bang our of order. She has to deal with it, not pass the buck.
School has a responsibility to safeguard. if your son is being threatened, they are not safeguarding. They can ban parents from the premises if they are threatening kids too.
So, go and talk to her. Be clear, this is repeated behaviour, it is bullying, she needs to tell you her plan to keep your ds form being bullied by this child.
Put everything in writing. keep a log of incidents, in your log, keep a log of times you have spoken to teacher, note what was specifically promised by the school.
If the class teacher will not take it seriously, ask for a meeting with the head, again, in writing, outline what you have done so far, ask her to tell you how she will be safeguarding you child. The threat of bringing in a gun is not only scary for your child but does raise some red flags.