Alan, I was able to locate a 1909 source that contains a couple of references that support your belief that the bridge mentioned as "Bluett's" by those Alabama soldiers (and an unknown mapmaker) was also, and more properly, referred to by the local population as "Blewett's Bridge."

The book, A History of Columbus, Mississippi, During the 19th Century
by William Lowndes Lipscomb and Mrs. Georgia P. Young, was published by the United Daughters of the Confederacy, Mississippi Division. Stephen D. Lee Chapter No. 34, Columbus, Miss.

The two references follow:

pg 25: “ … Market Street, eighty feet wide, crossed Main Street at right angles, and at its southern extremity was a continuation of the lower Tuscaloosa road, which running diagonally across the squares left the town at the Palmer Orphanage, thence south to a ferry across the Luxapalila at a place where Blewett’s bridge, built in 1837, formerly stood. This road was the first over which the stages passed bringing the mail and passengers to Columbus.”

pg 55: “Prior to 1837, on the Tuscaloosa road, at the place where Blewett’s bridge was built, a ferry was established by Tapley Oldham and Kincaid, which was the principal crossing over the Luxapalila.”