Final answer:
The pocket-sized device is called an inhaler and is used to self-administer a specific dose of a bronchodilator medication.
Step-by-step explanation:
The pocket-sized device that directly applies a specific dose of a bronchodilator, which a patient can self-administer, is called an inhaler. Inhalers are commonly used by individuals with asthma or other respiratory conditions to deliver medication directly to the lungs. One example of an inhaler is an albuterol inhaler, which contains a bronchodilator medication called albuterol.