Pick over the beans to remove any stones or bad or broken beans. Rinse thoroughly. Place the beans in a large bowl and cover with plenty of cold water. Soak overnight at room temperature or in the refrigerator if your kitchen is warm.
Drain and rinse beans and place in a 7 1/2-quart pressure cooker, making sure not to fill more than halfway but adding enough cold water to cover by 3 inches or following the manufacturer's instructions.
Wrap the herbs and garlic in a 6-inch square of cheesecloth and tie to enclose. Add the carrot, celery, onion, a drizzle of olive oil, and salt. Close and lock the pressure cooker and set it to high pressure. Turn the heat up to high and when the cooker reaches full pressure and the pressure button is fully raised, lower the heat to medium and cook for 7 minutes.
When time is up, release pressure using the natural method -- that is, move the pressure cooker to a cool burner and wait for the pressure to come down on its own (about 10 minutes). For electric pressure cookers, if the pressure has not come down in 10 minutes, release the rest of the pressure using the release valve.
Remove and discard the cheesecloth bundle and vegetables and drain beans. Serve beans warm, drizzled with olive oil.
Save the bean liquid for storing any leftover beans for up to 4 days, or use it in risottos and soups.