A family by the name of Bouse shows up in a database of Catholic parish records from five parishes south of Cork City, Ireland. In those parish records there are examples of it being transcribed as Bowes. It looks more like Bowes is used there as a variant of Bouse rather than the other way around, or is simply a transcription error based on pronunciation, but a closer look suggests that this Bouse family may have pronounced their name like Bowes because they had very early roots as Bowes.
Over in England, by the 19th century the Bouse surname was rare, appearing mostly in southeast England, primarily Surrey, with a small population north in Lancashire. While there is also a Bouse concentration in Lanarkshire, Scotland, the Scottish were less likely to emigrate to southern Ireland than to northern Ireland, while the English had a long history of settling southern Ireland. Meanwhile, it's not clear whether these Scottish Bouse were related to the English Bouse family or have separate Scottish origins.

Bouse in England and Scotland by Actual Numbers and County [1]
These Bouse are rarer than and appear likely to be a variant of Boase whose origins are in Cornwall, but who, as can be expected, were later recorded "spreading throughout England." [2]. While Boase, like Bouse, is rare by frequency in England, they both appear in relatively significant regional concentrations in Lancashire in the north and Surrey/Middlesex/Essex in the southeast. It appears likely these are branches of the same Boase family that spread from Cornwall.

Boase in England and Scotland by Actual Numbers and County [3]
Interestingly, the Boase Family Genealogy Site for North America states that in early Cornwall, “the name was at first usually spelt Bowes, but it is also spelled, like most names at the time, in a variety of ways; and the spelling Boase became a common one in the 18th century.” [4] Since the Boase family records in Cornwall begin with Bowes in the 16th century, it's not clear whether they are a branch of English Bowes from northern England, but given the wealth and influence of branches of Bowes in northern England, my guess is they are. DNA studies should help clarify this over time.
It is believed that the Bouse of Cork emigrated to Massachusetts. See separate Boase and Boas One-Name Study and Boase Family Genealogy Site for North America (tracking only descendants of Boase from Cornwall).
A German Bous/e
A fellow researcher who belongs to the Bouse family of Cork shares this:
When I invertigated the movement of the surname in to the United States some of the Bouse's that arrived there came from Germany, Austria and Czechoslovakia. In the German state of Saarland there is a town by the name of Bous. There is also a small town in Arizona called Bouse or Bousewash. As German history involved religious wars just like other European countries it is possible that people fled from one country to another to avoid these conflicts.
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1. Archer Software, British 19th Century Surname Atlas, database on CD.
2. Boase, Charles William and Boase, George Clement. An account of the families of Boase or Bowes, originally residing at Paul and Madron in Cornwall, 1st Ed. William Pollard, Printer, North Street, Exeter. 1876. URL: http://books.google.com/books?id=rC0AAAAAQAAJ&dq=An+account+of+the+families+of+Boase+or+Bowes%2C+originally+residing+at+Paul&q=+Bowes#v=snippet&q=Bowes&f=false Date accessed: 4 September 2010.
3. Archer Software, British 19th Century Surname Atlas, database on CD.
4. Boase Family Genealogy Site for North America. (URL: http://home.roadrunner.com/~boasefamily/index.html Accessed 26 Nov 2011).