The difficulty comes with the inversion of the sentence. Your brain doesn’t recognize that there are two items in the bag until you finish reading the sentence. Naturally, you read it like this: In the bag was money the boy had given to the old lady, and in the bag was a note…. If you write it in standard form you understand right away that “were” is technically correct: The money the boy had given to the old lady and a note that showed her forgiveness were in the bag. In the bag were the money the boy had given to the old lady and a note that showed her forgiveness. This form though considered correct sounds forced and unnatural. The singular form is what you HEAR everyday….I don’t think that you can really call it wrong…..However don’t choose the singular form on a language test if the sentence is inverted. A similar situation arises when you invert the sentence using “There is” There is money and a note in the bag. Or There are money and a note in the bag. Money and a note are there in the bag.... The plural is formally correct. There is money and a note in the bag… This form is widely used and, in fact, is more common among writers than “There are money and a note in the bag.” .....even though the plural form is considered correct in many classical grammars. If it is used more often than the supposed correct form, can it really be wrong? I don't think so.

To my ear, 'were' sounds utterly wrong. I would use 'was'. I don't know how to explain it, though! It might be because it is a list of single items, and/or because the 'and' separates them. What was in the bag? The money was in the bag and the note was in the bag. One of each.

I'd go for "were". It's plural: the money and the note. Though the money is uncountable this "were" will define both " the money the boy had given to the old lady" and "a note that showed her forgiveness".