If you’re going to do this (which I do sometimes) I would rinse with hot water first and then make sure to seal them in a clean bag. I keep a large ziplock in my pump bag and will occasionally wash it through with a soapy cloth if it ever gets any water spots/milk in it and leave it open on the bottle rack to dry
The fridge hack saved my sanity while exclusively pumping. I have a container that I store my pump parts in after use and sterilise both my pump parts and the airtight container once every 24hours. Baby is now 16 weeks and I've been doing it since about one month.
I found a lactation consultant after my daughter and she actually recommended putting everything in the fridge, rather than washing between pumps. It was a game changer! Still reduces bacterial/microbial growth. Just make sure to sanitize after, at least once a day.