If you're fit enough then cycle to Cape Town! If not, here's what the various airlines are charging to transport your bike to the Cape Town Cycle Tour (previously known as the Cape Argus) 2020 (note that the prices below are for 1-way flights, and you need to double them to get the airfare for a return flight):
Mango Airlines : R350 per bicycle & R400 per tandem bicycle
SAA : R350 per bicycle
British Airways operated by Comair : R350 (in 2018)
FlySafair : R285
Kulula : R370
Please take note of the special drop-off and pick-up location for your bike. As it is a massive operation at all airports they usually have special locations that can accommodate a large number of bicycles.
Whereas cyclists generally arrive in Cape Town over a period of several days, most leave CPT on the Sunday/Monday - this means that on returning it's more likely that your bike will arrive after you.
Here's some tips which will help avoid your VIB (Very Important Bicycle) from getting damaged during transit (although, it's still entirely possible, so do take out insurance). Note that different airlines have different rules for how to pack bikes, so be sure to study the rules of the airline you're flying with, but in general, the following applies:
Get a bicycle box to pack your bike in (some airlines allow bicycle bag) - this is a requirement of the airlines, but also protects your bike. You can get hold of the right shipping box at a bicycle shop.
First lower your seat completely to the bottom
Remove all electronic parts (e.g. speedomoters) and put it in your carry-on bag
Remove the pedals or twist them to face inwards.
Let the air out of the tyres (probably because the cargo section of the plane is not pressurised, and we don't want exploding tyres mid-flight).
Turn the handlebars to face the opposite way to when you'd be cycling.
The number of cartridges of pumps with non-flamable 2.2 CO2 allowed per passenger varies per airline (typically 2 or 4) - they are considered to be dangerous. They may only be taken as hand luggage, and if you try check them in or get them in the cargo with you bicycle, they will be confiscated.
Spare wheels need to be properly packed.
Wheelbags will not be allowed on board flights as hand luggage, and must be checked in - if you require an extra bag for this then you'll fail some airlines' "1-bag challenge" and have to pay for the extra bag.
Because the box with the bike in it will be checked at security, make sure you can open it, reveal the contents to security, and close it again.
Any equipment not complying with hand luggage limitations will not be allowed on board with you.
Mark the box and the bicycle with your contact details and flight details.