It's all good info above.
As with the above posters, I've done plenty of West Africa travel by public transport. My travel in that region was mainly ten years ago and more. The following applies to the lower, bumpier, dustier end of things because you can likely deal with new buses on good roads just fine. Mainly generalities because you are not asking about specific routes.
Try to pick a dry time of year. Rainy season makes difficult roads impassable.
Arrive as early as possible, as suggested above. Use your common sense as sometimes (rarely) the kids at the gares routieres try to stick you on a vehicle that isn't optimal for you, etc. Most other travelers can be relied on to take your side regarding these issues, or (rare) attempts at price gouging, etc.
If you have a choice, check vehicles for roadworthiness--bald tires, etc. If the tires are bald and you won't be going faster than a few kph anyway, maybe it doesn't matter.
You may "leave" several times before you actually leave. First to stop for gas, then to visit various people before leaving town, or to pick up passengers and cargo. Patience is key.
Some drivers know quite accurately how long a trip will take, how many kilometers between towns along the route, etc. Others on the same route have no idea, but will tell you anyway.
You may need to switch vehicles several times to get to where you are going, as with a stagecoach. Sometimes your own driver will try to switch you, for helpful or selfish reasons. Sometimes it pays for you to switch because another vehicle appears in better shape, or seems likely to leave sooner than the one you're in. As with any other calculation, you may be very mistaken as to what is in good shape and what it not, when it will leave, whether the driver is competent, etc. Enjoy!
On arrival, if the place you'll be staying is on the way (and sometimes even if not), the driver may stop or even make a detour for you. On some routes this will cost extra. On some routes you must tell the driver where you will get off, as this is what everyone does. On some, it's just a favor from the driver.
I tend to stick everything in plastic bags inside my luggage. (I make sure to take the bags with me when leaving the region.) Plastic helps keep out the dust, and any water or livestock urine that may creep in through leaky roofs.
Your luggage may be strapped to the roof of the vehicle. There may be a tarp or there may not be. Consider a shell to cover your luggage against dust and rain. If you are susceptible to lung or sinus issues or have allergies, consider a homemade mask against the dust. If you dislike loud music--I mean bordering on (or actually) painful--consider earplugs.
Avoid night travel where possible. Bad roads, speedy drivers and imperfect headlight maintenance can make for frequent accidents. People get concerned about political/criminal incidents (which can also be more of a problem at night), but the likelihood of an accident is far greater.
If you expect and can roll with good and bad surprises and factor them into your overall travel experience, public transport can be a blast. You will meet and (with a bit of French, Portuguese, etc. as needed) have some conversation with a range of people you would never be exposed to on an overland trip or in a hired car. The sense of solidarity that develops on a long trip only increases with any adversity you may face. And the resulting stories will make friends and family laugh for years to come, especially if the roadtrip was especially horrible (Labe-Koundara, Agadez-Zinder, Dori-Tera, etc., etc.).
