Stephen,
Well, for starters, there were at least three Pike County Burbridges in the Confederate service: Bill, Clinton, and John Q. "Jack" Burbridge. I seem to recall from reading that these three were brothers. I would hazard a guess that Sara was named after Colonel John Q. "Jack" Burbridge, one of the most proficient behind-Union-lines recruiters that Missouri had. He was also a crackerjack soldier and well respected not only by his men but by his superiors as well.
The following are references I found that tell about the Ashley fight where your ancestor was killed. I haven't checked lately, but perhaps there is a little bit of biographical detail in them about Captain Moses Beck:
--U.S. Government, "Official Records of the Union and Confederate Armies," and etc. series 1, vol. 13, page 261;
--"A Fight at Ashley, Missouri," "Central City and Brunswicker," newspaper at Brunswick, Chariton County, 11 Sept. 1862 (on microfilm in at least two places in MO);
--Mills and Company, "The History of Pike County, Missouri," Des Moines: Mills and Company, 1883, pp. 274-6;
If you wish to examine these, the first reference is readily available in nearly every library, and the other two can be viewed via interlibrary loan.
I enjoyed writing about your ancestor (and the Burbridges), and I wish you well in your hunt for information.
Bruce Nichols