Not a bad question at all. In some other thread I questioned how easily Tom Hagen got a flight to LA on short notice.

In Michael's case, the family likely had connections with the railroads, airlines, etc., and could make arrangements for travel on a moment's notice. As for taking the train, Michael was in Tahoe, but he had to go to Miami to see Roth and then make his surrise visit to Pentangeli, and then go to Cuba.

My best guess is that he traveled from Tahoe overland to the nearest plac where he could catch a train to Miami. Roth was told Michael was on the way because he was met by Johnny Ola, and the visit to Roth's house was not supposed to be a surprise. As for the bodyguard, IMHO Michael already suspected Roth, and he needed someone who would protect him AND kill enemies in Cuba, as he did (or in Roth's case tried).
Since Roth had already failed in his effort to kill Mike, he would not have tried again knowing Mike was on his way to Miami. Back then he could probably have traveled by rail using an assumed name.

I think he took the train more to keep Pentangeli off his trail so he could make the surprise visit.

Always keeping his enemies closer, Michael visits Roth to misdirect him into thinking Michael believed Pentangeli tried to kill him, and clearing this with Roth in advance, presumably to keep the Rosatos from taking over the olive oil business while the Corleones cleaned house.

Once this was done, Mike goes to NY to tell Pentangeli to go along with the Rosatos, and to help him take his revenge against Roth.

Then its on to Cuba, for a meeting everyone knows about.

Roth definitely had spies, however because he was keenly aware of when the 2 million reached Havana (the spy probably being Fredo).