When the scene opens, Bolingbroke has captured Bristol Castle, where Bushy and Green have been hiding out.
Bolingbroke doesn't want there to be any confusion, so he tells everybody why he's sentencing Bushy and Green to death.
First Bolingbroke accuses Bushy and Green of corrupting the king and coming between him and his friends and family members (including Bolingbroke).
Then, since no political drama is complete without a sexual scandal, Bolingbroke implies that Bushy and Green both had sex with Richard, making a "divorce betwixt his queen and him" by breaking "the possession of a royal bed."
Finally, Bolingbroke says that Bushy and Green helped King Richard steal his land from him, which basically stripped Bolingbroke of his identity as a "gentleman." (Remember, a nobleman's name and all his power come from his land.)
Bushy and Green say they'd rather die and go to heaven than live in England with Henry Bolingbroke running around.
Bolingbroke orders Northumberland do his dirty work for him by making sure Bushy and Green are put to death. Northumberland is all over it.
Bolingbroke turns to York and says he wants to make sure the queen is treated fairly. (How considerate of him.)
Then he says something like, "Okay guys, time to get back to our uprising. If we work hard now, we can party later."