Bernadine is another ill-fated friar. (You'd almost think that Marlowe has a grudge against the Catholic Church.) He's all buddy-buddy with fellow man of God Jacomo—until, of course, money comes between them.
After Abigail spills about her dad to Bernadine, Bernadine and Jacomo confront Barabas about his crimes. Like Jacomo, Bernadine loses interest in his ever-so-noble quest for justice when Barabas offers to convert to Christianity and, oh yeah, bring his money to whichever monastery he joins.
So we're not too surprised when Bernadine eats it in the end. (By eats it, we mean "ends up strangled.) Bernadine, like Jacomo, is just one more hypocrite. Although he's supposed to be selfless, devout, and celibate, he's just as self-serving and corrupt as everyone else.