We might reasonably expect the English Bowes surname to arise as a locational name associated with Bowes village or parish found in Country Durham, once considered part of northern Yorkshire. It's quite possible that some families took the name Bowes because they lived in this area. The Bowes of Streatlam Castle and Bowes-Lyon fame, ancestral to the Queen Mother, are reputed to have done so early on.  We see this reflected in their earliest recorded ancestors going by de Boughes, de meaning from and boughes being a spelling that was sometimes used for the parish in early times. 
However, when mapping the Bowes distribution using 1881 census data a stronger possibility for this surname's English origin than Bowes village or parish emerges. The census data show the Bowes name clearly reaching its highest frequency—by a long shot—considerably south of Bowes parish and village, in the Poor Law Union of Helmsley. This holds true whether mapping by actual numbers or frequency.
English Bowes Surname, 1881 by Poor Law Union, using Archer's Surname Atlas
It's possible—though far from proven—that Bowes village and parish, as well as most Bowes surnamed people who are apparently from the Helmsley area, take their names from river bends that were prominent topographical features at these settlements. The Norse word for bow (bend) is bogi. (You can hear how bogi is pronounced today at Google Translate, where the "g" is sounded.) These river bends and the word bogi bear associations — sometimes clearer than others — with the name Bowes. While further research is called for, for now I'll note these observations:
River bends would provide more water frontage close to a settlement than where a river doesn't bend or bends less. This might be seen as the most desirable place to settle along a river. Were Norse descendants responsible for naming one of their early families after the river bend in Helmsley? And were Norse descendants also behind naming Bowes parish bogis, prior to it becoming Bowes? All we can do is speculate and continue research. If this is true Bowes would be a topographic surname, one of the earliest types.
We need many more English Bowes men to join the DNA project and see if there are strong signals of Scandinavian DNA among them.
Interestingly, a separate researcher of the English Bowe has been arriving at the same kind of topographic explanation to explain the origin of English Bowe.
Since no Bowes or variants are recorded as land owners in the Doomsday Book from 1085-6, these Bowes must have acquired their holdings later. Records show they are ancestors to the above-mentioned aristocratic Bowes of Streatlam Castle and Bowes-Lyon fame who took their name from Bowes village and parish. That line of Bowes may well be Norman while others may have earlier Viking origins.
 missing cite
 'Parishes: Bowes', A History of the County of York North Riding: Volume 1, pp. 42-29 (1914). (URL: http://www.british-history.ac.uk/report.aspx?compid=64715; accessed 11 July 2010)
 "Helmsley," Wikipedia (URL: http://en.wikipedia.org/wiki/Helmsley; accessed 12 Jul 2013)
 missing cite
 Surtees, Robert. The History and Antiquities of the County Palatine of Durham: Compiled from Original Records Preserved in Public Repositories and Private Collections (1816-1840). 4 volumes. (London: J.B. Nichols).