What is the ruling on someone who speaks to a girl in the street intending to propose to her?

Imam Al-Bukhari, in his Kitab Al-Nikah (Book of Marriage), mentioned the permissibility of a man being alone with a woman in the presence of others, citing the hadith of Anas ibn Malik: "The Prophet, peace and blessings be upon him, was alone with a woman from the Ansar and said to her: 'By Allah, you are among the dearest people to me.'" Al-Hafiz Ibn Hajar explains that this 'privacy' (khulwa) was in the sense that those present could not hear the conversation, not that they were out of sight. It is permissible to converse secretly with a non-mahram woman when there is no fear of temptation (fitna) and the conversation is limited to what is necessary.