In ACLS, we give Adenosine as a rapid bolus in narrow complex tachycardias (i.e., AVNRT). It is rapidly cleared (half life of less than 10 seconds). With that said, it would make sense to be avoid giving the drug in patients with asthma (where bronchospasm is the main feature of the disease) while giving it cautiously in patients with COPD where bronchospasm is not the underlying presentation (such as emphysema).
A long list of drugs can cause bronchospasm, including adenosine, but it's far from contraindicated as the incidence of bronchospasm with adenosine is <1%. Albuterol, which of course is commonly given to COPD'ers, has been shown to produce bronchospasm at a rate of 15% in one study (in 2.5mg neb doses).