Hallo Dave,
The wooden bridge at Khwai North Gate is doable with the Bushlapa, yes.
The area has had excessive rains this year and the main transit road (Khwai-Mababe-Maun) is in very bad condition - it is dry now but very deep potholes. On top of that, much of Moremi is under water, and there is currently a detour in place from South Gate to Xakanaxa, you cannot use the main road - and this detour has some very deep water crossings, people are currently changing their bookings from South Gate to Xakanaxa. And there is still plenty of water coming down towards the Delta, water levels are rising daily.
Have a look on Facebook at the Moremi Game Reserve Sightings group, there is lots of info there on the roads in Moremi. Also look on DriveBots for other roads in Botswana.