The main wildlife-watching circuit crosses the Bridge of God to the park’s namesake savannah, but the road is so atrocious that many tour companies prefer not to come here; nobody will attempt it when it’s wet. It takes about three hours to reach so there’s no chance of wildlife watching during the morning hours unless you camp.
Another option is to boat across and then walk, though because of past armed robberies the park turns permission for this on and off with some regularity. You’ll need to bring an armed scout from the park headquarters. A boat from the association costs Birr1800 for up to six people and can cross in about 90 minutes.