How long can I keep the milk in a bottle after the baby touch it?

I read in books and on the internet that bottles with milk that touched the baby’s mouth, should be washed asap – preferably immediately.

My wife says that we can keep the bottle up to two hours. She says that, that’s what happened in the hospital.

So, who’s right?

Ps 1. Does it matter if the milk is formula or breast milk?
Ps 2. Does it matter if the milk bottle is kept in the refrigerator or “outside”?

Thank you.

Daniel