From "The Bauerle Family Tree" (1985), by Dwane V. Norris.

SHORT HISTORY OF THE BAUERLE FAMILY
         
Frederick Gottloeb Bauerly was a residence of Zurich, Switzerland.  In their 
community, Swiss watches were made.  Frederick made the watch gears, then passed
on to the neighbor to do an operation, and each in the area had a part to the 
completion of the watches.
         
In the research, Bauerle/Bauerly were found in Switzerland and Wuerttemberg, 
Germany, but found none connecting our roots.
         
Frederick had at least one known son, John M. Bauerly, who was born 1804 in 
Zurich, Switzerland.  It is not known when John moved to Germany, but John 
married Carolina W. Deyle in 1832 in Germany.  John and Carolina had three sons
born in Warbach, Wuerttemberg, Germany: John Frederick Bauerly born 27 March 1833,
George Gottlieb Bauerly born 14 August 1834 and Charles William Bauerly born 
15 November 1837.  John M. was a wagon-maker and gunsmith by trade and came to 
America in 1837 to set up a business.  John first settled in Saline, Washtenaw
County, Michigan and was engaged in Wagon-making.  Subsequently, he moved to 
Jonesville, Hillsdale County, Michigan where he worked at his trade until his 
death.  Many wagons, had done good services all through Michigan and some crossed
the plains to California, as there was a great demand for this thorough work of 
wagon making during the gold excitement of 1849-1850.  While in Jonesville, 
John had lost contact with his wife and three sons and assumed that something 
had happened to them.  Sometime in the early 1840's he married Mrs. Anna Myers.
John M. and Anna had three children: John B. Bauerly born 1844, Elizabeth Bauerly
born 1849 and Emma Bauerly born 1850.  At a later date John finally made contact
with Carolina and his three sons in Germany and thirteen years after he arrived
in America, on July 1851 Carolina and their three sons arrived in America. 
The youngest son Charles William Bauerly was 13 years and 8 months at the time 
they arrived in the U.S.  It was a great undertaking for Carolina and the three
boys, as they arrived in America after forty-three days on the Ocean, eighteen
days journeying from New York City to Jonesville, Michigan by the way of the 
Great Lakes.  Carolina had lost contact with John and where he was living.  
After arriving in America and finally in Jonesville, the children were enrolled
into the Jonesville schools for four months, and then Carolina and the three sons
moved to Washtenaw County, Michigan where they attended school. John M. Bauerly
introduced Carolina to a friend of his and later 21 June 1852 Carolina married 
John Schneeberger in Freedom Township, Washtenaw County, Michigan.  
John (Johannes) was also born in Switzerland.
         
Carolina and John Schneeberger lived in Freedom Township and to this union 
one daughter was born: Carolina Schneeberger born 27 October 1853 in Washtenaw 
County, Michigan.

[...]
         
The surname was originally spelled Bauerle, because the pronuncation was like 
the grain Barley, the "y" replaced the "e" making the surname Bauerly.  Sometime
in the early 1900 Edward Henry Bauerly got the brothers and uncles in the Clinton
and Ingham Counties to change back to Bauerle.  However, Edward's son Glenn 
Bauerle changed back to Bauerly.  At the time he was living in Portland, Oregon.
As a result some remained with the spelling Bauerle and others spelled their
surname Bauerly.  Charles William Bauerly and his sons all spelled their surname
Bauerle; John Frederick Bauerly, Sr.and his family were of the Bauerle spelling,
except he remained with Bauerly; George Gottlieb Bauerly's family spelled the 
surname Bauerle except George and his son Daniel Bauerly and his family.  Those 
that remained with the Bauerly spelling were: Jonesville, Michigan families; 
Daniel Bauerly of Cleveland, Ohio and his three children in Chicago, Ill.; 
Glenn Bauerly of Portland, Oregon; John Frederick Bauerly, Sr. of Lansing,
Michigan and George Gottlieb Bauerly of Lansing.

RDB note: I'm not sure I agree with that comment about the pronunciation; 
I believe the correct German pronunciation is "bow-er-leh".  Also, the name 
appears to mean "little farmer".