Future Press game guide description: "The Bigoted Old Man lives across the street from Arianna, Woman of the Night, in the Foggy Alley of the Cathedral Ward. He's just an ordinary citizen of Yharnam, complete with the endemic suspicious streak, and wants nothing to do with you until he overhears you direct his neighbor Arianna to a place of refuge. At this point he'll challenge you to convince him that he should follow her and when he thinks you're not looking, he'll sneak off to the location opposite the one you suggest."
From his clothing and behavior, we can be confident that the Bigoted Old Man is an ordinary citizen of Yharnam. Yharnamites in general don’t share much with outsiders. They keep to themselves and most seem to blame outsiders for the situation Yharnam is in, reveling in tales of “pompous” outsiders suffering for their ignorance. It’s also no secret that Yharnamites are heavy users of blood, as in Yharnam; blood is more intoxicating than even alcohol. Like a drug that has no diminishing return, successive transfusions recall the first and are all the more invigorating for it. The Bigoted Old Man is no exception to this peculiar Yharnam madness.
The Bigoted Old Man is also just that; bigoted. His opinion is that all outsiders are liars. He is clearly prejudiced against Arianna, saying "her sort's probably just fixin' to thieve some of your coin" and "bloody wench, they shoulda moved her ages ago", implying that they (the Healing Church) should have killed her. He is also deeply suspicious of the blind beggar, believing his motives to be devious, and as mentioned earlier, he certainly does not trust outsiders to Yharnam.
The Bigoted Old Man will give the player a couple "nuggets" of advice throughout the night. He will tell you that the blind beggar is not to be trusted, and that he has a murky past. He will also tell you that Arianna resents Adella, despising her for having what she doesn't, referring to Adella's special blood. We know that the beggar is in fact trustworthy, only wanting to help the people of Yharnam and while he may have a murky past, it does not show in his behavior. We also know that Arianna is not resentful of Adella, but rather the other way round. Interestingly enough, the Bigoted Old Man will only go to the opposite refuge that you suggest to him. So if you tell him to go to Iosefka's Clinic he will go to Oedon Chapel and vise versa. Basically what this all points to is that when talking to the Bigoted Old Man, keep in mind that whatever he says the opposite is true.
When he is killed the Bigoted Old Man drops 3 Pungent Blood Cocktails. While this cocktail can be used to lure away the beasts, it seems most likely he had it up his sleeve because he is in fact a user of blood, just like many other Yharnamites, and the amount he drops implies that he is a heavy user of blood.