As given that some volume of water has been dispensed say "x mL"
The initial weight of bottle =8.4376 g
The final weight of bottle + water =28.5845 g
So weight of water transferred = 28.5845 g - 8.4376 g = 20.1469 g
Now there is a relation between density, mass and volume
density = mass / volume
Therefore
Volume = mass / density
So volume of water dispensed = mass dispensed / density =20.1469 g / 0.9967867 g/ml.
Volume of water = 20.2118467 mL