I do not see Napoleon fleeing Civilized Europe for underdeveloped country of Bolivia. First he would placing his life in danger from any of the thousands of Spanish loyalist. Remeber his forces have just been pushed out of Iberian Peninsula the previous year. During their timeline Spain the French had killed hundreds of thousands of Spanish, looted the country and kept their king in prison while putting a French puppet on the Spanish throne. So he would not risk his life going to any Spanish speaking country. The people regardless of their desire to be free of Spanish rule would not welcome Napoleon. Heck if he survived one week I would be shocked. Anything he ate would be suspect of poisoning, any person there would be suspect of having a knife or gun to kill him.
No South America or Carribean are out. That leaves us with US. Let’s look at the dates of Napoleons time at Elba and War of 1812. Napoelon fled in feb 1815 while war ended in feb 1815. So does Napoleon simply stay the whole iOTL time at Elba or he leaves early? He would not show up at US doorstep just as the country signs peace treaty he know he has no chance of success getting accepted. But what happens if he shows up earlier say late to middle 1814? Let’s say he hates Elba so much that within a few months he makes his escape arrives in US. There he would be heralded by the War Hawks in Congress as a “savior” to help the US vanquish the British from American continent. President Madison might be against it but if enough people support Napoleon becoming the US next “General Washington” he would be powerless to send him back to Europe.
What happens next?
As for British Abilitity to transport troops across the Atlantic I am sorry but who ever stated it not possible is not aware of the BN size and power. The British Navy could bring over tens of thousands of troops. With Napoleon in America there was no danger in Europe and with British economic capabilities they could of also hired thousands of seasoned mercenaries to supplant any troops they send over.
FYI Spain in 1820 was about to transport thousands soldiers from Spain to the Americas to recapture the revolting colonies. The only reason they never sent them was the troops revolted and refused to leave Spain. So if a broken down country like Spain could transport thousands of soldiers Britain could of transported ten times more.