In the past (couple of years ago) immigrants were allowed to take along their motor vehicle tax-free into S.A. But times may have changed, so the best would be to inform yourself at the S.A. Embassy in London.
For a limited period of time you may of course import your bike on a carnet basis. Here the Automobile Association would be the best contact. There are lots of posts regarding carnets etc. here on the HUBB.
The cheapest way of transport is via seafreight, but harbour fees on top of the freight charge are quite annoying. Airfreight is more expensive, but easier to organise. Just as reference: I paid 1,300 Euros for airfreighting my bike from Munich to Cape Town last year.
It probably would be the least hassle if you buy a bike in S.A. and sell it, when leaving the country.
Only when we pause to wonder
do we go beyond the limits of our little lives.