I have a NalPak TuffPak
http://www.nalpak.com/TuffpakSportCases that was originally designed for hauling around tripods for camera crews. Now they are commonly used for guns, bows, and all sorts of other equipment. When you are traveling to Africa you will see several people with them on your flight. The cases now are fairly recognizable as "gun cases", but so are most cases that size that are going to Africa. Typically, your plane will be filled with hunters and mission groups, not golfers, so anyone who is half way knowledgeable will assume there is hunting equipment of some sort in large, hard-sided baggage. I have transported bows (and rifles too) in my TuffPak on a number of occasions without any trouble. I always stuff some of my extra gear (clothes, boots, jackets, knives, arrows, etc.) into the TuffPak until it is either full or at the maximum weight for the airlines because the TuffPak is very protective and also has wheels that will roll. The golf club case will be similar, although it does not have the same level of protection or security as the TuffPak. With guns those are important factors, but with bows the golf club case will be more than adequate.
I would recommend a good take down bow case for your bow with even a little added padding inside the bow case to keep the pieces of the bow from knocking against each other and damaging the finish. The best bow case I have used for traveling to Africa is the Safari Tuff Gazelle case
http://www.safarituff.com/predator_bowcase.html. I also have a couple of the Rhino bow cases that Rod makes, which are great cases for most uses, but they are not as protective in my opinion as the Gazelles. Another hint: take along a strung bow case with you so your bow doesn't get banged up while you are riding around Africa in the vehicle over rough terrain. You and everyone around you will be happy you brought the strung bow case, because otherwise you will be trying to hold the bow in your hands, or people will be diverting their time and attention to protecting it, or it will be getting damaged. The strung bow case will keep the bow protected and will allow everyone to keep their attention on hunting. I have tried all the cases, and the best I have found for a strung bow with a bow quiver is the one from 3Rivers
http://www.3riversarchery.com/Cases+Bow++Strung+Recurve+Longbow+with+Quiver+Case_c43_s193_p0_i1154_product.html. Even if you use a back or side quiver (and I often use a Safari Tuff Arrowmaster or Duiker side quiver), the 3Rivers case I mention will work fine for bows without the quiver and will give you the option of later using it with a bow that sports a bow quiver. In that regard, I often take along my Arrowmaster or Duiker quiver as well as my bow quiver and use the side quiver as my arrow case. It is an easy matter to add a little extra padding around parts of the side quiver to provide full length protection for the arrows, and then you have an arrow case that you can actually use as a side quiver when you get to Africa.
Make sure if you have screw-on points or broadheads that you remove them from your arrows for travel. Use proper protection from you broadheads for the safety of everyone concerned, including baggage handlers and security staff. Depending on the type of broadhead you choose, there are various ways to pack them. I would be happy to discuss that with you if you want some additional information. You can PM me. Make sure and bring some light duty webbing straps with delrin buckles. The straps work well in some packing applications, for rigging up bow cases in the vehicle, etc. They are cheap, small, and light and have many uses. Just don't get them too short. You can always cut them down, but you can't add length.
There is significant red tape to deal with if you are bringing firearms into South Africa, and it is worthwhile to hire one of the local groups to help smooth out that process. But bringing in bows and arrows is no problem whatsoever, especially trad bows. I assume you will be taking a take down bow(s). They don't even want to look at those or any of your associated archery equipment like arrows or broadheads.
Because you will be on international flights, you normally will get 2 checked items and you carry-ons. Most of the airlines allow 50 pounds for each checked bag, so you should not have any problem with your golf bag. Having your other bags on wheels is nice for airports, but the wheel systems add weight and bulk and prevent you from collapsing your other bags when you need to, so I tend to take non-rolling soft-side bags for everything else besides the hard case that will transport the bows, arrows or firearms. Lots of other people use wheeled bags, so figure out what works best for you. Make sure to check with the airlines you will travel on for weight restrictions on your baggage and then weigh your bags at home so they are not overweight when you arrive at the airport. You will not be happy if you get charged a bunch extra for a few additional pounds that you could have eliminated by using non-wheeled luggage or leaving some unnecessary items at home. I don' know what your airline arrangements are, but you might think about flying to Washington, DC, Dulles airport and then taking South African Airlines to Johannesburg. I have made those flights many times from Oklahoma (I notice you are just south of me in Texas), and they work well.
Whatever else you do, make sure to pack all your optics in your carry-on bags. Those are expensive items that can be broken and are also prime targets for theft by baggage handlers. Also, take a change of clothes and a substantial jacket in your carry-on just in case your luggage is misplaced for awhile. Wear your hunting boots on the plane for the same reason. Even if most of your gear gets to you late, you can still get out and scout the hunting area if you have minimal gear with you. Nothing will be more important to you than your hunting boots, because they are irreplaceable. In that regard, make sure your boots are well broken in and very comfortable, and make sure you have worn them extensively just before the hunt in the most demanding conditions so that your feet are broken into the boots too. More hunting trips have been ruined by foot/boot problems than by any other cause. You should take a big supply of the best adhesive bandages made in case there is any problem with blisters and sores on your feet. If you need more specifics, feel free to PM me.
A trip to Africa requires good planning because you can't just go to the local store and get what you need when you get there. But with the right equipment and preparation, your hunt will be one of the highlights of your life.
Allan