Best case scenario is that the South could remain mostly (if not solidly Democratic) to the present day. On the Presidential and Congressional level, Florida, Texas, Virginia and North Carolina were trendng Republican starting with Dwight Eisenhower's election in 1952. This was due to northern Republicans migrating to these states, forming suburbs and bringing their voting habits with them.
This is happening now as well, only with the opposite results. Same with Georgia. Obama won VA, FL, & N.C. and came close in GA. Texas is also a lot less 'safe' for the republicans than a lot of people seem to think. The growing Hispanic population and influx on young college students who then stay after graduation could eventually put Texas in play, though it'll take a good while if it ever does.
I think the GoP needs to realize that the tea party is only hurting them in the long-term due to this. If the south becomes more moderate over the next 20 years, or perhaps even a state like Virginia becomes reliably blue (as I think it's trending toward) then they could find themselves in a tough spot. They need to be actively trying to turn voters in states like Wisconsin, Iowa, Michigan, Minnesota, etc.
As for the timeline... busing is a key, yes, but you also have to consider that Clinton did well in the south as late as 1996. It wasn't until 2000 that the GoP really took over as the majority party in the deep south. I think a lot of that had to do with the Clinton/Lewenski scandal and the reaction of social/religious conservatives in the south. It's telling that Al Gore couldn't even win his home state of Tennessee in 2000.
Also, 9/11 was big. It helped to create more clearly divided demographics between the south, which was more pro-Bush and pro-military and the more liberal states where you were more likely to see protests against the war in Iraq and Bush.
This helped lead to the democrats being perceived by many in the south as a party of bleeding heart liberals who, in their view, didn't support their country/President in a time of war. Now, I don't agree with that view, but being from the south I can tell you it's what a LOT of folks down here were thinking at the time.