Question for anyone who bottle feeds - breastmilk, formula, whatever!

LO is 11 weeks and starts daycare on Monday, so I'm pumping 5 bottles a day now. I wash at night and put them on a Boon Grass to dry. Regardless of whether I steam sterilize or not, they are ALWAYS still wet when I get up in the morning. (Honestly, they are more wet when I use the steam sterilizer.)

Do I need to dry them before I pump into them? I'm not talking about a few drops, but they are VERY wet. I'd rather not have to run the dishwasher every day, if I can avoid it, hence hand washing and air drying.

Any tips/tricks to streamlining this process and getting things dry faster? Thanks!