Any ideas on connecting flights to Bahamas without transiting in US, UK or Europe.
I am in South Africa.
You can fly from Johannesburg to Nassau via São Paulo (Brasil) and Panama City. It'll take over 30 hours, and some of the flights in there are not scheduled every day of the week.
You could also fly via Istanbul (Turkey) and Toronto (Canada). Takes nearly 48 hours.
But if you do that just to avoid the requirements for a visa, even though the US requires visas for all transiting passengers, the situation in the UK or the Schengen Area is more relaxed. Most passengers do not need a visa at all as long as they stay airside, and those who do need a visa will usually only need an Airport Transit Visa (again, only if they stay airside).
If you are absolutely insistent on avoiding the US, UK and EU (and if Canada is also not an option), there is a very round about way to get from South Africa to The Bahamas and the rest of the Caribbean.
South African Airways has a direct flight from Johannesburg (JNB) to Sao Paulo, Brazil (GRU). From GRU you can then self connect to a COPA Airlines itinerary from GRU to Nassau, Bahamas (NAS) via Panama City, Panama (PTY).