This question was asked nearly a year ago and unfortunately wasn't answered it appears. However there was an answered follow up question that seemed to shed some light on the anti-nepotism laws that were passed after the Kennedy administration.

https://www.reddit.com/r/AskHistorians/comments/64bqhi/what_was_the_public_reaction_when_jfk_appointed/

Yes, the press was very disturbed by this, and JFK and RFK both knew this was going to be their reaction, but Papa Joe made them do it.

It's only a short section of this novel that addresses it, but in "A Hero for Our Time" by Ralph G. Martin, the author notes that "Much of the press responded negatively. The Chicago Tribune quoted President Woodrow Wilson's letter refusing to appoint his brother as postmaster in Nashville, Tennessee: 'It would be a very serious mistake for both you and me.'" (Martin 256)

The reason it didn't become a political time bomb? That good ol Kennedy charm. The Kennedys announced this appointment during a yacht party, where Bobby was very natural and charistmatic. To quote Martin's book again: "Chuck Roberts of Newsweek agreed that 'Bobby could not have been more charming',". (Martin 255)

In fact, a lot of people who JFK asked for advice on this matter told him to do it, saying that it could only hurt Bobby, not him, since both the brothers were so charming and popular.

Ultimately there isn't too much detail on how exactly the press responded. It seems while the press didn't respond well, people generally admired Bobby enough that it blew over relatively swiftly. I wish I could give more detail on how exactly it blew over so fast, but the book only gives it a few pages.

No info on the actual senate hearings.

Ralph G Martin's "A Hero for Our Time". If you like Kennedy, check it out, it's fantastic.

Side question, how good was Robert at his job? Was it justifiable for JFK to do this because Robert did a good enough job? Or were the anti nepotism laws put in place after this because Robert wasn’t good for the position?