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well it kinda depends on which route are you on. If you are on the good ending route then along with the bloody cloth you MUST have 2 emblems
1 from defeating the first boss (that skull demon) and the other can be brought from the auction (saving the master quest).
once you have both the emblems, go to the bull temple. You might have seen a secret room on the right side of the temple. Enter the room with a torch and be ready for some magic. I won't really spoil anything to you but I will tell you if you feel like something is off or something else should've happened while you enter the secret room, enter that room multiple times until you see something that is related to thane. What happens after is a secret because of, you know, spoilers. For further details you can download the free fanmade guide uploaded.
just a tip for the demon city, when you start the working week I'd suggest you to work in slums in the morning, as a beggar in afternoon and at love hotel at night. I used that way and it got me more than 300 of that bevocr/ currency. And at the time of bidding, try to add just +1 or +5. Jumping to higher numbers like +10 or +15 won't benefit you instead it will drain your currency.
Also buy a lot of beer before you go into the dungeon/city. Drinking Alcohol gives "lust" and with higher "Lust" you gain more Bevocr from the Love Hotel. So always get your Lust to 90+ before going into the Lust Hotel.
P.S Do NOT wear/use Murphy's Hand at all...... except maybe Bossfights you struggle