Bodega y Quadra was eager to participate in an expedition scheduled to depart from the San Blas naval base for the Pacific Northwest in 1775. Bruno de Hezeta was in command of the Santiago and Juan de Avala was captain of the Sonora when they left San Blas on March 16, 1775. Avala became ill soon after, and Bodega y Quadra was promoted to commander. The captain worked alongside his seamen, a necessity with such a small crew. They sailed north, out of sight of the coast for lengthy periods. The expedition was soon plagued by scurvy, and they recorded a conflict with the coastal peoples during an on-shore water and firewood-gathering trip on the Olympic peninsula.
Hezeta wished to turn back with his sick men but Bodega y Quadra hoped to continue north; the two vessels parted on July 30. The Sonora reached Kruzof Island, Alaska, on August 17 and turned back on August 22 due to scurvy and harsh weather conditions. They arrived back in settled Spanish territory, sailing into Monterey on October 8. The expedition had reached 58' North latitude and had gathered information about vast regions that could be added to their coastal charts.
The viceroy of New Spain was enthusiastic about the 1775 expedition and began to organize a second voyage before the Sonora had even returned from the first. Wary of the ongoing American War of Independence, they postponed the expedition, giving them time to construct the Princesa at San Blas, and to send Bodega y Quadra to purchase Favorita in Peru. They left on February 11, 1779, Ignacio de Arteaga commanding the new Princesa and Bodega y Quadra the Favorita. In mid-July, they landed off San Elias Cape (Cape Elias), pushing further north than their first expedition. They turned back after reaching 60' 13´ North latitude, arriving in San Blas on November 21, 1779.