Obviously I know nothing about law as spunk has pointed out, but how would Trayvon admitting he beat up a bus driver for no reason, bragging about it, not be admissible as evidence regarding his character. Not saying it is or is not, just looking for clarification.
The defense would be introducing evidence of Trayvon's prior bad acts to try to show conduct in conformity with those acts. It's prejudicial effect on the jury would outweigh the probative value. It's a classic example of character evidence that should be inadmissible. Obviously the judge makes the decision, so it's up to her. But I'd be shocked.
It's the same reason when a convicted felon is on trial for a new felony, you can't bring up their prior convictions until the punishment phase. You don't want someone convicted on what they did in the past.
Edit: I actually could see a relevance objection as well. If Zimmerman didn't KNOW about Trayvon's past run-ins, then why would it have anything to do with his mindset (i.e. stand your ground, self-defense, etc.)?