Oh, that's an exurb of Atlanta. That explains everything!
Except where the eponymous bridge actually is or was.
The only waterway in the whole area seems to be a little wetland-creek that's run as a culvert (so there really is no bridge!) under HB Drive, and HB Road changes names just across I75 to the east and ends at Jodeco Rd not far to the west. Is the "bridge" the I75 Overpass!?
If I look at old maps... Old railroad right-of-way seems to have been used to build I75 in the area, so... ...Yeah, I got nothing. Most detailed map I could find from before the highway went in was a 1956 map by Shell that put the area in question just outside of the bounds of their Atlanta metro map.
...Unless the bridge wasn't on Hudson Bridge, and the road was so named because it was the way TO Hudson's Bridge!? Which would mean the bridge was probably a flimsy wooden bridge on Jodeco Rd over Pates Creek where the causeway is now, which somehow feels worse than if there were never any bridge anywhere at all.