There were also Baeuml (varient spellings' this is likely the original, as I've seen it in chronicles, published in Germany, spelled this way--actually B-A (w/ umlaut over A, which makes it "AE"-U-M-L)-), in the FALKENAU district (now Sokolov, Czech Republic).
Falkenau, as well as Bishofteinitz belonged to the former Austrian crownland (until 1918)-then Czechosolovakia until 1938 when annexed as the German Sudetenland--then after 1945 Czechoslovakia; now Czech Republic). This is the "German-Bohemia" of which Tony wrote.
I have seen it in Milwaukee City Directories since 1851 (John BAUML, butcher ); 1856 John Bauml, Saloon @ Lake & Reed Streets) and then variant spellings thereafter, including 1885, where I have in research notes written an address of 492-16th Street and that there were 4 listings. There are still BAUEMLs in the Milwaukee area.
Several years ago, I had done some research on German-Bohemian surnames for the German-Bohemian Heritage Society and this name showed up often. I am going from memory, but believe I also saw listings for them in St. Joseph German Catholic Church, formerly located at 12th & Cherry Sts (records at LDS Family History Center, combined with records of St. Joseph's in Wauwatosa).
You may want to subsribe and post a query on the Rootsweb GERMAN-BOHEMIAN list and also visit the German-Bohemian Heritage Society website. Someone may have already researched this family.
By the way, if from the areas already suggested, you may find records/census info that give different areas of birth as either, Germany, Austria, Boehmen (Bohemia), as it changed so often.