Usually route taxis have a route printed on the side door saying what the route is. So you'd need one from your hotel to the roundabout/taxi park (or walk, if you are close), one to Sav and one to Black River. I am not sure where the taxi park in Black River is but since the bridge over the river is right downtown and that's where the boats are, I'm thinking it's not likely far.
A charter taxi is about 2 hours to Black River so I'd add some time for route taxis, since you have to change (and wait for one to fill). Although they do tend to drive faster so you might make up the time
Maybe take a route taxi around Negril once or twice first, if you can, to get a feel for how they work.
Small Jamaican $ is advised.