BELLARMINE; When did he live? 1542-1621
What was the mentality/worldview of your character? Conservative. He wanted to maintain the status quo to the Catholic church, not necessarily against new learnings, but against the way those learnings were presented that were contrary to the Catholic Church's position on the matter. So long as they had evidence, and could be fit in to the Church's teachings, then they were acceptable, but because bellarmine was not a fan of novelties, he did not like any huge shifts in power.  Actually was one of the true people who deserved his position, because he believed in acesticism, but ironically that stopped him from being pope, because many of his peers didn’t believe he would keep the papcy and  higher levels of the church at their same comfy positions and they might actually have to act out their beliefs. If he was active during the trial, what position did s/he take? N/A 
If your character lived before or after the historical trial, figure out what position they would have taken, if they had access to a time machine. Bellarmine would most likely rebuke Galileo, and demand more evidence/an explanation for this second infraction. A stern punishment might be in order, if Galileo did not recant, and something like exile, excommunication, or imprisonment else shy of death might be in order to get the point of "Strike 2" across to Galileo.