Just had an interaction with ireress and it states the runner loses 1 credit for each bp the corp has. My question is, can the runner choose to loose the credits by using the bad publicity credits? Or does it come out of the runners credit pool?

There is functionally no difference. Bad Publicity actually ADDS CREDITS to your pool when you begin a run - they aren't treated in any way differently to any other credits UNLESS you don't spend them before the run is over.

To clarify, you'd be a pretty weird runner to NOT spend your Bad Publicity credits hitting Iress because those credits will be lost at the end of the run while your regular credits will remain. Of course, if you're already involved in a game involving an Iress...

In essence, the function of Ireress is just to zero out BP credits.