Peace server, Wasteland tribe, zone 904, leave the tribe through the West gate, once outside the tribe head North West and cross the river, that's more or less the same path across the river the Shadow Bear took.
After I posted this bug report I went looking for the bear, and found it underwater near the north shore of the river, so it looks like this bear wont swim in any part of the river in 904.
I'm thinking it's a creature size issue, bears at max HP are huge in size, and I'm pretty sure this is a maxed out female as she hasn't gained any HP in months (despite my best efforts).
I did spot a couple of black bears and a shadow bear swimming in the main N>S river in zone 823, but I also watched a 280 female black bear walk under water to cross one of the small rivers in that zone (2nd from the North, and just East of the road).