Where are you going in Botswana? Are you staying at lodges and / or using their vehicles, or are you doing a guided / self drive tour where you have the same vehicle throughout the trip?
I go to Botswana every year and try to get out on safari when there. All the tour / lodge trucks I have seen have been open ones like this: linky
, so nowhere really to place a beanbag. I typically have a monopod with me in the truck, whether I use it or not just depends on the day. I don't have a head on mine, but use the tripod foot on my lens to rotate the camera if needed. If you are going on a guided tour and keeping the same vehicle, this may be a more enclosed truck in which case a beanbag may be more appropriate. You can get out of the trucks, but only at dedicated picnic areas, and IME there is nothing worthy of shooting that requires a tripod in these areas. The game reserves in Bots (Chobe, Makgadikgadi, Moremi etc) require you to be back in camp or have left the reserve by sunset / dusk, but private concessions may be different. Similarly, you can't leave camp / enter the reserve until sunrise / dawn. All the drivers I have been with shut the engine off when we stopped without anyone needing to ask them.
In the three reserves I have mentioned above, all the roads are sand / dirt. In the dry season they are dusty, but I have never had a problem with the dust. Be sensible though; don't change lenses until the truck has stopped and dust settled, clean your kit / dust it off when you get back to camp, if you notice lots of dust on your kit whilst out, blow / wipe it off, use lens caps when travelling at speed. Botswana IME is fine with a 70-300 on the whole, 70mm may be too long at times as there is thick bush in places, but on the whole I have found that I haven't needed to change lenses often.
I haven't been on safari in Zim or Zam, so no idea what things are like there.
Hope that helps you a little.