Hey CollabResearch,
It's great that you're looking to unlock the full potential of QuickBooks Online to further streamline your books. Bank rules are designed to easily categorize and add downloaded transactions based on the information we obtain from the bank. This data is most notably the amount, the description, and the specific bank account. The easiest way to match a transaction to a bill is to make sure the bill is already recorded for the same amount. This makes it easier for the system to automatically recognize the transaction, so you'll simply just need to click Match.
If you have any feedback about this functionality, you can send your comments directly to our engineers. Every time you submit feedback, you're helping us continue to build the best QuickBooks experience possible. Check out this handy article to learn how: How do I submit feedback?
Hope this helps!