The Amount field respects accounting "natural balance." Meaning positive does not necessarily mean a debit and negative does not necessary mean a credit.
Positive means an increase in the balance of the account and negative means a decrease in the balance of the account.
For a liability account, an increase is a credit. Putting a negative "expense" on the bill would cause that amount to become a credit to the account, which is an increase to a liability, hence it showing positive on the saved search.
Hopefully that makes sense, but if not, adding Amount (Debit) and Amount (Credit) to your search rather than Amount might make it show in a more understandable way.