Aroma is a crucial attribute for wine quality, particularly in white wines. Traditionally, the consumption of young white wines is recommended over the year following grape harvest due to potential aroma losses that would worsen wine quality. This study aimed to investigate the evolution of volatile compounds, odor activity value-based aroma notes, and sensory perception in Treixadura (Vitis vinifera L.) dry white wines during a 24-month bottle-aging period. Volatile composition was determined by gas chromatography, and wine sensory evaluation was performed by experts. Wine samples had similar volatile compositions at the time of bottling. The volatile contents of the wines were respectively 322.9, 302.7, 323.0, and 280.9 mg L−1 after 6, 12, 18, and 24 months of bottle storage. Most of the volatiles tended to maintain constant concentrations, or with slight increases in all families of volatiles except for acetates and carbonyl compounds, until two years after harvest (18 months of bottle storage) and, then, concentrations reduced sharply. After 24 months of storage in the bottle, the concentrations of terpenes, C6 compounds, higher alcohols, ethyl esters, fatty acids, acetates, carbonyl compounds, and volatile phenols were reduced by 32%, 47%, 11%, 39%, 50%, 74%, 41%, and 54%, respectively. The 18-month bottle-aged wines showed the highest concentrations of volatiles, as well as the best performance in the sensory evaluation, suggesting that a good balance of the aroma attributes was achieved on this date. In conclusion, the current study suggests that Treixadura wines expressed their maximum aroma potential two years after grape harvest.