I read a book, "Galileo's Daughter" that was not strictly about the heliocentrism affair, but gave enough of the details, plus what I thought was good insight into the surrounding social and political issues. One interesting political issue is that the Church hierarchy was facing accusations from lower level clergy, of being "soft on heresy" in the aftermath of the Reformation. Some people saw the Galileo affair as a test of whether the Church was willing to assert its authority or not. Also, Galileo had two trials, that were conducted under two different Popes. And some of the issues were clouded by the fact that it was actually hard to communicate between A and B in Italy. Apparently many of the letters back and forth were held up because they would not carry mail through towns that were under quarantine when a plague came through.

The text of Bellarmine's letter to Galileo is worth reading.

Note that I'm not defending the Church with my comments, but only documenting what I think was the technical difference between the Galileo and Bruno cases.