I have never seen Bić written on any documents
Quick look at site moikrewni.pl/mapa/ and I've found just one person with name "Bić" registered in Poland - more precisely in Bytom - town less than 100km from Krakow in the west direction.
Surname Bik is far more popular - 1132 people have that name in Poland.
Other names like Byk, Bikowski also exist in Poland
Rare Polish surname beside Bić is Bic - but it's presented either on the list of surnames in Poland:
Are these all variations of a name (sort of like Smith and Smythe)?
Probably. It happened often that Polish emigrants in America changed their names and surname "Bić" could be a good example - no "ć" in American alphabet, and very difficult pronunciation for Americans.