Breastfed baby getting bottle at daycare

Hi there I need your help/ advice. My baby was strictly breastfed until I went back to work. I gave her a bottle about five times before I went back to make sure she’d take it but she only ever ate 2-3oz at that point. My baby is 12 weeks old and about 10.5lbs.

At day care this week my sitter keeps track of how much she eats and today she ate 5oz, 5oz and then 5.5oz which is the most I think she’s ever ate. I am only pumping about 4oz 3 times a day when I’m at work. At this rate I won’t keep up!

My question / concern tho is if I’m pumping 4oz, wouldn’t that likely mean that’s max my baby is eating? I mean she can’t be eating 5oz from my boobs if I’m not producing that by pumping could she??

Can a breast milk bottle fed baby over eat?? I don’t know what to do. Please give some advice thank you!!!