Feeding schedule or on demand?

Ni

My baby is 2 months old. We do a mix of breastfeeding and bottles of breast milk. More bottles than breastfeeding most days.

Our pediatrician told us to start getting our babe on a schedule for feeding. 4oz every 3 hours during the day (he only wakes once at night). Prior to this he has done 3oz every 2 hours or on demand.

I’m having a hard time not just whipping out the boob when he’s fussy or rooting. I also don’t want to let “him run the schedule” as our pediatrician said. I’m also kind of worried that not feeding him on demand might mess with my supply.

What are you mommas doing for your 2 month olds? I go back to work in 2 weeks so he will have mostly bottles every day.