Getting Acquaintances to become Friends
According to Bulbapedia:
The main window of the PSS divides other players in three categories: Friends, Acquaintances, and Passersby. A Passerby will automatically become an Acquaintance if a Battle or Trade (including Wonder Trades ) is made with him/her: after trading or battling with a player already in the Acquaintances, a prompt to add them to the Friends group will appear.
So it seems that 2 Battle/Trades are needed in order to get the prompt.