Welcome to the WD forum Nick.
I'll just answer one of your questions, the one regarding riding through National Parks.
Unlike the USA Nat Parks (like Yellowstone etc) the Nat Parks in SA are actually Game Reserves. They are fenced and they have (most of them) the Big 5. Lion, elephant, leopard, rhino and buffalo. Lions will eat you. Elephants are protective of their herds and if you are on a bike they can easily kill you. Leopard usually only hunt in darkness. Rhino's are the size of a small compact car, but are usually docile. The Cape Buffalo is a very grumpy fucker, it's bigger than a cow, and will charge, spear you on it's horns, and trample your body into the dust.
Then there are many other animals in the Nat Parks too; impala (deer) zebras, giraffe, kudu's, countless other antelope, extremely venomous snakes (think black mamba, google it if you want) and countless other critters that can cause you very serious bodily harm, even death.
To protect you, the Nat Parks do not allow bikes inside them, except in very few special circumstances (like organised trips with rangers etc). That is just the way it is. An alternative to going on a guided tour would be to rent a car outside the park and use that to explore on your own time, but going on a guided tour will give you a much richer experience. The guide will point out the animals to you, and tell you a whole lot about them. Well worth the money and time.
And just some free advice. Plan on 30 days, but accept that Africa runs on Africa Time, so have a couple of weeks leeway planned just in case. Also, you want to stop and admire, photograph, and experience Africa. Take some extra time, take it slower, and you'll enjoy the trip a whole lot more.

I emigrated to the USA (sunny warm Florida

) 3 years ago from SA. But I still yearn for the beauty and splendour that is Africa...