You're on the right track when you say that it can be neutralized to form ions. Since acetate ions are charged, they are much more soluble in water than in organics. Therefore, if you wash your reaction mixture with aqueous sodium bicarbonate, the base will deprotonate the excess acetic acid, forming acetate ions. These acetate ions will migrate out of the organic phase and into the aqueous phase, removing them from your product when you separate the organics from the water.
Isopentyl alcohol is much more poorly soluble in water than acetate ions, and is much more similar to your ester in terms of solubility products. If you were to try a similar extraction to remove teh isopentyl alcohol, you would either leave a lot of alcohol with your product or lose much of your ester.