The type of clause in the underlined part of the sentence "The man, who I met at the bus stop, is a close friend of my father" is:

(2) Adjective clause

An adjective clause, also known as a relative clause, provides additional information about a noun (in this case, "the man") in the sentence. In this sentence, the clause "who I met at the bus stop" is an adjective clause because it describes or provides more information about the noun "the man." It tells us which man we are talking about, specifically the one "who I met at the bus stop."