Final answer:
Bassanio first encounters Portia through a mutual friend, as depicted in Shakespeare's play 'The Merchant of Venice'.
Step-by-step explanation:
Bassanio first encounters Portia through a mutual friend. In William Shakespeare's play The Merchant of Venice, Bassanio learns of Portia, a wealthy heiress, from his dear friend Antonio. Intrigued by the descriptions of her beauty and virtue, and the challenge of winning her hand through a test set by her father's will, Bassanio sets out to Belmont with the purpose of attempting the riddle of the caskets. He does not meet her at a royal ball, during a marketplace encounter, nor strictly by solving a riddle initially—it is the latter that he must do in order to win her hand in marriage.