I understand your anger and frustration. Let's discuss your issue:
1. You made a mistake by confronting them
You played right into their hands. How did you end up in that situation? By letting your emotions get the better of you. Don't do that again. Your words radiate anger - you have to let that go.
You're dealing with mean, petty, conniving people. If you walk into that meeting with this attitude they've got you.
2. Get help from the union
Meet with a union rep ASAP. Explain exactly what happened, tell them every detail of their behavior, and the exact words and attitude you used that day. They will back you up, but you have to give them ammunition.
Your union rep can probably coach you on how the meeting will go. What they will ask, what and how you can answer. Even if they don't, always keep one thing in mind: be polite and calm. Do not display frustration, or anger.
3. Ask for your union rep to attend the meeting
I wouldn't walk in there without someone in my corner. Calmly and politely demand that your union rep attend. Maybe explain it to your boss in person that you will not attend if your rep is not allowed.
4. You can't pin the blame on them
I'm assuming you don't really have proof of the bullying you've endured at their hands. We'll get to what you can do about that later. In the mean time however, you have to set your goals are priorities.
Proving they are liars is probably not on the table.
You want to come out of this alive to fight another day, as it were. In other words, you're avoiding being fired. You should probably admit that you were very frustrated, and spoke in a heated manner - never admit that you were angry, or spoke aggressively!!! If they ask you if you spoke loudly I wouldn't even admit to that. Say simply I was frustrated and passionate. Nothing else.
Try to explain the situation objectively, but don't seek to cast the blame solely on them. On the contrary, defuse the situation as best you can - by admitting partial blame.
This is what happened: ... (your story, delivered in a neutral voice, without casting blame) ... I have to admit that this was a very frustrating situation for me, and my attitude reflected that. I was never aggressive, nor would I ever be. If I spoke harshly, I apologize, it was simply in the heat of the moment. My employee record will show that in the 14 years I've worked here I have never once had a complaint lodged against me. (this is when the rep can jump in and defend you further)
Anyway, you see where I'm going with this? Remain neutral, don't cast blame, as you will once again appear to be "on the offensive". You are trying to refute claims of "verbal aggression", so that's the last thing you want to do.
5. In the future
This whole situation might spark an entire chain of events (meetings, consultations, etc.) During this time you might be working alongside these managers the same as always. Don't allow yourself to be baited into another conversation. Keep your interactions with them short, and polite.
If the bullying persists (which it probably will), document it. I don't know where you're from, but in Canada (Ontario) it's actually legal to record a conversation as long as one of the participating individuals is aware that a recording is being made (in this case yourself). Find out what the law says in your particular area. Maybe in a future conversation get a witness of your own to back up your bullying claims. Better yet? Get a new job. These people are entrenched, and they have it out for you. I don't think working there is going to get any easier from you from now on.
Good luck, and remember: get help from your union!