OK, the bad news here is that on some level, you've done what you can for the moment. It sounds like, for whatever reason, the principal is not going to be able to be helpful in the way that you want her to be. It sucks that the onus for action is always on the victim, but that's the way the system is structured. So, first, get a copy (in writing!) of the school and district's bullying policy (everyone has one these days. And if there legitimately isn't one, YOU can be the force to create one.) There is likely something about it in your school's parent handbook.
That document will likely spell out what steps you as a parent need to take to register a complaint and ensure that it is resolved appropriately.
In the meantime, you are not powerless. Neither is your son. Sit down with him and make a plan. Bystanders are as powerful in bullying situations as the bullies themselves. Your son is surely not the only victim of this bully. Gather his friends, and his friends' parents, and talk about how they as a group are more powerful than the bully. And then document, document, document. Enlist your son's friends to observe and document. "On Oct 26th, X said this and did this in the hallway between 4th and 5th period." Document for, say, a month - or a week, if that gives you enough to establish a pattern.
Don't be afraid to make noise, mama bear. There are resources for you, here's just a couple that I found.
Rally the bystanders! Some recent studies have shown that changing the response of bystanders (those who witness/watch the bullying) is the most powerful deterrent to bullying - far more effective than punishing the perpetrator.
Just do your best to stay respectful, to follow the protocols set out by the school and the district for reporting things. And if you don't get an appropriate response from the school, escalate to the district. Or the county. I understand you have transportation constraints, but at some point it will be useful to actually appear at the principal's office. NOT to have the bully punished, but to work with the school to ensure a safe environment for all students.
Your son is not alone, and what is happening is not acceptable. I know that is cold comfort for him when he gets assaulted in the hall on the way to math class, but it's still true. Go, mama bear!