Being honest here, there were so many times where Billy should have realized that the Landlady was crazy, and even the most naive person should have realized the Landlady was a threat.
The most obvious instance where Billy should have left immediately was when he say that there were only two names on the guest book, and when he heard that even after 3 years, the two guests were still there, which if you add up the cost, is quite strange. If he had only asked to meet one of the guests, he probably would have known for sure the Landlady is a murderer and ran away easily, as he is 17 and the Landlady is probably in her sixties.
Something that I find strange is why the woman even asked Billy to sign the guest book, which was completely unnecessary, as Billy was obviously naive and new to staying at inns. I think that in no way it was because signing the guestbook is the law because this Landlady straight up murders and stuffs all of her customers.
Something else that I find funny is that that Billy told the Landlady that he was heading to the Bell and Dragon, which is kind of an insult to her. This is because Billy is basically announcing to the Landlady that his was more inclined to go to the Bell and Dragon, which was technically a direct business competitor with the Landlady, as they were on the same street.