Reasons for the HIV-1 epidemic
if Bushmeat practices (eating meat from non-domesticated animals, in this case HIV-infected fruit bats) have been the same for centuries, why has HIV only really spread in THIS century?


We can't really rule out the existence of similar epidemics in the more distant past. In fact, almost certainly they were transmission events from bushmeat (not necessarily of the same virus). The thing that made 20th century different, as the other commenter rightly says, is the mobility. Previously, such transmissions would have lead to local epidemics which would have run their course - leaving super-controllers or individuals with immunity and killing everyone else. And since most of the African cultures haven't left a written record we wouldn't know about such isolated local epidemics. Not to mention that in the unlikely event of such records existing they would hardly be scientific - the disease would be most likely attributed to "evil spirits" or some other supernatural cause. 

So, it is really the mobility, the public policies (mass vaccinations by colonial authorities that used the same syringes repeatedly) and the fact that we can retain information in a much better way which make the HIV epidemic different than the ones that almost certainly have happened in the more distant past.