Unfortunately, there is no clear answer to this question as there is no research about whether it is safe or not. Until recently, the standard answer was to discard any breastmilk left in the bottle after a feed. However, recently it has been suggested that it might be okay to store breastmilk in the fridge for a short time. The current thinking is that bacteria growth is possible, but not likely, because fresh breastmilk has anti-bacterial properties, and a breastfed baby has a strong immune system to deal with any bacteria that do grow. If the breastmilk has been frozen and thawed some of these properties are lost. The final choice is yours; let common sense be your guide. If the baby's next feeding of pumped breastmilk ends up being 7 or more hours later (because he slept through the night, for example) or the breastmilk was stored in the fridge for several days before being fed to the baby, you may choose to err on the side of caution. To avoid wasting precious breastmilk, mothers usually prepare bottles with a small amount, 1 to 2 oz (30 to 60 ml), to start a feeding.  More breastmilk can be added to the bottle if needed.