The surname could possibly be a reference to a place name. There is a town by the name of Bodzanów about 70 kilometers to the northwest of Świniarsko. (There are actually several villages with this name around Poland, but this one is the closest.) There is a also a town farther away in Świętokrzyskie Voivodeship, (north of Małopolska Voivodeship) known as Bodzentyn, which has been around since the 1300s. So, it's possible that the family name originated as a way to tell other people "this family is from Bodz... village."
I do have evidence that the name was NOT changed when Michael came to America - the name shows up fairly frequently in the 19th century Roman Catholic Church records of the Diocese of Tarnow.
©2014, copyright Emily Kowalski Schroeder