Is it really not possible to create Bill Payment transaction saved search showing both the paid bills and the credits applied? Cant show the credits applied

In a template?

Edited: in a saved search

Surely they would show up under applied transactions and applying transactions?

No. They don't unfortunately. I also tried paid and paying transactions

You'd have to do a Bill Saved Search with applying (or applied to...I can never remember). Probably your issue is that I'm pretty sure even though you choose a credit to apply when making a bill payment, the credit has zero association with the payment. In the background, it's actually being applied to the bill.