" I have thought about e-mailing the owner or the directors but I'm afraid that will make things worse for my daughter."
Your own words.
If your child is attending a school where you feel so -- afraid? Ignored? Powerless? -- that you would say this, then you need to find another school. Truly. If talking to the adults who are in CHARGE of this school would somehow make things worse for your child, there is a much bigger issue here: The school is being run very badly.
That issue aside: The mere mention of the word "shooting" would, in most any public school today, bring about the instant removal of that student until the comment could be investigate and, possibly, the child gotten into some form of serious help. Have you told the principal and teacher and counselor -- all three in one meeting, not just one or the other -- exactly what this boy said? Word for word as your daughter related it? I would tell them immediately and inform them that in most schools any such threat -- however impossible it seems, however much the attitude is "he doesn't mean it for real" -- would STILL mean the child would be dealt with the very same day.
Being compassionate toward a clearly troubled child does not mean being dumb about safety.
Sadly, the boy probably needs therapy and other interventions. It sounds as if he has emotional, developmental or mental issues that need help. He's more to be pitied than feared, but your child's safety comes first. If the school is telling you that "It's only words, your child is safe," tell them that your child's mental state is not safe; she is afraid, and no child should be told that it's OK or normal to go to school in fear.
If you know other parents who have had issues with this boy, I suggest you all go, together, to the principal and teacher and say that your children are in fear. Let them know that as parents, you DO feel for the boy, and you do understand he may have issues that are beyond his control and call for help and compassion. But your own children are fearful, and that matters too, and you need for some specific interventions to take place so that this stops and both he and those he is bullying are able to learn in a safe environment.If you must, threaten them with this: It's a private school, and you can take your private school tuition dollars and walk away to somewhere else.
A boy in my daughter's class in first grade had some issues with this kind of talk and with shoving girls and hitting boys etc. (though he was not older or bigger than other kids). The intervention was swift and firm at school. His desk was moved so it was touching -- not next to, but actually touching -- the teacher's desk. He spent part of each day doing classwork at a table inside the principal's office, not as a punishment for any specific behaviors but as a matter of course in his school day. He was closely monitored by teachers when in gym or at recess. Problem? Instant removal, no appeals, off to the principal's office to do classwork. It took a team -- his classroom teacher (who was very experienced), the principal, the vice principal (who sort of oversaw him in general), the school counselor (who intervened with his parents) and the teachers of gym etc. -- to nip this in the bud. He quickly learned he could not behave in certain ways or he would be instantly removed from everything and thrust into the principal's office for ALL of the day. Very importantly, he also got counseling and other forms of help with his aggression issues.
So it takes a lot of work. Is your school willing to do it? Are the boy's parents? Are other parents willing to work with you to impress on the school that this is not something that can be tolerated, whether or not the parents of this boy say they'll sue?