Is it permissible, in Islamic law, to use dhikr (remembrance of God) in permissible amusement, such as saying "Bismillah" (in the name of God) at the beginning and "Alhamdulillah" (praise be to God) at the end?

If amusement is permissible, then uttering "Bismillah" (in the name of Allah) at the time of amusement becomes permissible. It may even be recommended sometimes in matters such as riding animals, and when a husband approaches his wife. It is also permissible for one entering a swimming pool, for a thrower when throwing, and for an athlete at the beginning of their permissible sport.