PC Gamer has reported that crashes in the game are caused by the interplay between Bonfires' lighting and the game's cloth textures, which can be simply too beautiful for certain graphics cards.
Turning the lighting levels down apparently seems to fix the problem but the game doesn’t automatically save the change, meaning you have to reset this when you restart the game. There have been complaints on Reddit and Steam forums that say the game crashes either after the first bonfire, or when players approach Firelink Shrine.
The problem doesn’t appear to affect players in the same way and could possibly be linked to the class you play as. Bandai Namco is directing reports of issues to its support team, and has yet to confirm what the issue is, or how players can address it. I’m sure once the team has looked into the issue there will be an update to resolve the matter.