Can asthma be diagnosed during a regular doctor visit or multiple visits required?

Not necessarily : It depends how typical your symptoms are.

Yes, if...: Yes, one can be diagnosed with asthma, given the history (the story): symptoms, worsening factors, change over time or with medication, associated illnesses, family history, examination. Particularly if one can measure reversibility of airflow obstruction following a bronchodilator with an accurately performed pulmonary function test. FeNO testing a bonus.