He comes in out of nowhere after the Tahoe shooting and is joined at the hip with Michael until he's killed in the hospital in Havana.

--What was his connection to Michael so that Michael immediately trusted Bussetta with his life?
--Why didn't Michael use Rocco and/or Neri?

Your thoughts?

Well, Rocco was under a cloud after the catastrophic failure of his security regime, and, I would imagine, Michael left Neri - whose loyalty was beyond doubt - to keep an eye on his family. And Rocco.

As for Bussetta, I have no idea. He can't have been an old Family associate because Fredo had never met him before. As you point out "He comes in out of nowhere after the Tahoe shooting ..."

I've always assumed that Bussetta is one of Don Tomassino's men, so that Michael is drawing from the well he trusts the most. In the flashback scene where Don Ciccio is killed, there is an extra man who leaves the car and helps carry Tomassino to safety. I've wondered if that, in Coppola's view, is the young Bussetta.

Did anyone else notice that .......

Michael could have also used the same Travel Agency! that arranged Vincenzo Pentangeli’s miraculous appearance at the Senate hearing

I seem to remember Turnbull posting [or similar] –
Michael wanted to show Roth that Michael didn’t suspect Roth was complicit in the Tahoe shooting and Michael was still looking inwards for the traitor in the family As such Michael couldn’t trust Rocco and/or Neri [of course! All for Roth's benefit!]

Besides Michael turning up in Havana, Roth’s territory, with just Bussetta was to reaffirm to Roth that Michael and Roth’s relationship was still good

I agree with all here:

Both Rocco and Neri weren't beyond suspicion of being complicit when Michael left Tahoe.. As Michael told Tom, right after the shooting: "All our people are businessmen. Their loyalty is based on that." Also, by not taking them to Havana, he was signaling Roth that he hadn't yet identified the traitor. Fredo's gaffe at the Superman show revealed his treason. Technically, it didn't totally dismiss the possibility that Rocco and/or Neri were in it with Fredo. But, I think Michael knew that neither of them would have been stupid enough to side with a dunce like Fredo--or that Fredo would have had the coglioni to approach them.

I also agree that Buscetta must have been part of some old Sicilian loyalty connection that Vito passed along to Michael before he died. He might well have been connected to Don Tommasino.

I reckon unarmed Bussetta out of nowhere, did pretty good improvising

Yeah, we once had a poster on this board whose sign-in was "Death by Coathanger."