Bulldog would get put into the Sting/Luger angle, trying to play one side or the other. If he's a face, he probably winds up getting some matches with Luger and filling in for Luger in tag matches. WW3, he tosses one of them and at Starrcade, he interferes somehow, intentionally or not and it sets the track for at least the following month. He could probably take Renegade's slot as fourth face, giving him someone like Pillman or Benoit for a little bit and then maybe Jarrett. He'd get some TV title spots with Regal, for sure, and with Finlay. Would be lost in the shuffle when the nWo kicks off.
If he goes heel, he's a Dungeon member and probably spends time with Sting or Booty Man while being the devil on Luger's shoulder before moving on to a Horseman, again maybe Jarrett and eventually Mongo. Probably ends up with the TV or US belt by summer and turns face around the Bash. Stays in the midcard, gets spraypainted a few times, and then just becomes another guy.