Sheikra is over the far side of the park and usually the busiest although Rhino Rally is always the busiest due to such slow loading. When I have been to BG (over 20 times in 6 years) I have always found it to be quiet up until mid afternoon when you can get more locals arriving. It does depend on the weather of course and weekends are always busier. Personally I would head to Rhino Rally first (not the greatest but interesting if small queue) one thing to do is ask the guy at the entrance if the water feature is working, if it isnt I dont think its worth going on unless you can walk right on. After RR head towards Sheikra, after doing this you can do the water rides over there if you want or head to Kumba. I wouldnt bother with Python (a simple corkscrew coaster) after Kumba you can either get the cable car over to Egypt or walk picking up a few of the animal attractions on the way. In Egypt you have Montu (my favorite coaster!) if you can get the front then do that, in fact if there are no queues try every row because believe me they are all different. The back row especially! After Montu head back towards the entrance (pick up your return bus ticket at guest services) and then head towrads Gwazi. I like Gwazi but the last few times I went only one side was open which meant long queues, as with all woodies dont eat just before as it rattles you to the core.
Other things for me are the train ride if you want to relax for about 40 mins, the busch beer tent for your couple of free beers, spending a couple of dollars in the water cannons shooting people on the Congo River Rapids and of course just wandering around soaking up the sun.
Just beware that this is a huge park so your feet will take a beating, if you are planning to do the water rides I would take a change of clothes otherwise you might be a bit uncomfortable.
Anyway, just enjoy, I have used the shuttle numerous times and find it relaxing and doesnt take that much longer than driving yourself, they even did a shuttle last year for halloween which was even better.