I have no specific info on Peter Bosche family. There are however two Bosche sisters who came to America in 1841. They are Catharina Bosche who was born 5 Aug 1815 and Maria Anna Bosche who was born 7 Mar 1819. They were the daughters of Heinrich Bosche and his wife, Anna Maria Luxenburger and were born in the village of Scheidterberg which is near the German French border and the old town of Saarbrucken.
Catharina Bosche married Johann Micka and the family settled in the Platteville area. Anna Maria Bosche married Johann Valentine Pitz and also settled in the Platteville area.
Perhaps your Peter is a brother or nephew of the above.