Juba may very well be related to the biblical name sometimes given to dogs in the Southern USA (likely, as Amos mentioned, after the famous general), but there's no demonstrable relation to the phrase used in the song, which probably didn't belong in it in the first place.

Let me mention another instance from another version of the song, Bold Reynolds (Journal of the Folk-Song Society IV (1913) p.290. Francis Jekyll got it from a Mr Heygate at Rusper, Sussex, in 1910. Mr Heygate sang "joyful hounds", but that isn't my point. He also sang

"They ran bold Reynolds five hours or more, to Partridge town sixteen"

Now, I can easily imagine a thread here earnestly debating the most likely location of Partridge Town, and the occult significance of that "sixteen" (an early post code?) Compare other examples of the song, however, and it becomes clear. Mr Heywood had misheard the words when he learned them. Happens all the time. There was no "Partridge Town sixteen". Bold Reynolds (many people didn't know that Reynard was a literary name for the fox, and simply substituted a name they did know) was chased through parishes sixteen.

Simple; and you do it by looking at the evidence provided by other examples of the song, not by rushing out looking for Ordnance Survey maps. Start at home and work outward if you need to; proceeding in the other direction will lead to all sorts of bizarre speculation which may well be interesting, but will confuse the hell out of people who look at this thread in the future...