"To finish the bottle" means to consume all the contents of a bottle, typically referring to alcoholic drinks, before considering oneself done with it. Full definition
If your baby doesn't finish a bottle of formula within one hour, toss out the remainder. (babycenter.com)
If your baby doesn't finish a bottle of freshly pumped or refrigerated milk, you can offer it to the baby again at the next feeding. (exclusivepumping.com)
After finishing our bottle of pink bubbles, I decided to get a head start on gifts this year since I'm usually always super last minute. (sosageblog.com)