It's an English name, not a Dutch name.

Bledsoe
English: habitational name from a place in Gloucestershire named Bledisloe, from the Old English personal name Blið (a byname meaning ‘cheerful’) + Old English hlaw ‘mound’, ‘tumulus’.
http://www.ancestry.com/facts/Bledsoe-name-meaning.ashx?fn=&...



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Note added at 48 mins (2008-01-17 01:36:27 GMT)
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http://www.houseofnames.com/xq/asp.fc/qx/bledsoe-family-cres...