I highly doubt it's a parasite, as the vast majority of parasites that attack our bettas aren't black OR that big. If his behavior is pretty normal, I would say that's a bit of shredded ventral fin. One way to help clarify what it is is to cup him and look at him from underneath (hold the cup over your head). That way, you may be able to see if the black bit is hanging from his body or from his ventral fins.
If he is pooing normally and the poo is normal in appearance, I would just observe him for a day or two more. 1 tsp of epsom salt per gallon won't hurt him if you'd like to just treat him proactively.