Allium cepa L. is one of the most abundant vegetable crops worldwide. In addition to its versatile culinary uses, onion also exhibits quite interesting medicinal uses. Bulbs have a high content of bioactive compounds that are beneficial for human health. This study intends to develop and optimize two appropriate ultrasound-assisted methods for the extraction of the phenolic compounds and anthocyanins present in red onion. A response surface methodology was employed and, specifically, a Box–Behnken design, for the optimization of the methods. The optimal conditions for the extraction of the phenolic compounds were the follows: 53% MeOH as solvent, pH 2.6, 60 °C temperature, 30.1% amplitude, 0.43 s cycle, and 0.2:11 g sample/mL solvent ratio. On the other hand, the optimal conditions for the anthocyanins were as follows: 57% MeOH as solvent, pH 2, 60 °C temperature, 90% amplitude, 0.64 s cycle, and 0.2:15 g sample/mL solvent ratio. Both methods presented high repeatability and intermediate precision, as well as short extraction times with good recovery yields. These results illustrate that the use of ultrasound-assisted extraction, when properly optimized, is suitable for the extraction and quantification of the compounds of interest to determine and improve the quality of the raw material and its subproducts for consumers.