But for others that may be looking.
Fleming Bard (b 1820 PA) married Anna Coffman (b 1820 TN) in Polk Co Missouri 24 Feb 1842. They are living with her family in the 1850 census. They had seven children. the oldest daughter Louisa married Richard Vrign (b Wisconsin 1842 I believe). The most well documented son is James Madison Bard who had a son named George Fleming Bard and many sources totally confuse the Grandfather Fleming with the grandson George F.
Given the nature of where they lived in 1860 according to the census on Lost Creek I went looking for all I could find about the geography and history of the area. The village of Dayton (Newton Co.) was not really named that during the war not being platted until 1869. The best period map is Lloyd's Official map of Missouri published 1861 which you can see at http://memory.loc.gov/ammem/collections/civil_war_maps/subject.html (search for Missouri and it will be listed as Missouri 1861 in the index list.) Seneca is listed on this map as Sparlinburg. The railroad shown was listed only as a projected route but is very close to where the FRISCO line ended up.
Dayton (See Racine). (--Gazetteer of Missouri, p. 401.)
Dayton, (later Racine, q.v.)., was the name of a post-office which is now known as Racine. It was named for Dayton, Ohio. (--Place Names.)
Dayton or Racine, was 12 miles from Neosho on Lost Creek, and was the site in 1869 of Richard Gilstrap's saw and gristmills and wagon and blacksmith shops. The town of Dayton was platted on the Southeast quarter of the Southwest quarter of Section 1, Township 25 N, Range 33 W, by Edgar Shroeder, surveyor for Richard Gilstrap, owner, and the plat recorded April 27, 1869. When Senecal Village came into existence old Dayton lost many of her citizens, except what were purely local. (--State of Missouri, History of Newton Co., Goodspeed, 1889, p. 390.)
You mentioned the Senaca-Dayton Road which is shown on contemporanous maps as running along Lost Creek very close to where the railroad was eventually laid down. It appears that this road was the "highway" between the border of the Seneca Indian territory and Neosho. Hardly a straight line but easily traverses the geography alongside the creek. The issue is when you start looking at the time frame 1862 1863 this part of the country traded hands almost weekly given who happened to be moving along the road.
The first question I tried to winnow out was what was the proclivities of Mr. Bard? Given extended family information, particularly information about the Coffman clan, specifically Thomas L Coffman, as well as the Bunch(e) clan, I'm pretty well conviced Fleming Bard was likely a "Union Man".
There were nearly daily brushes with a number of "bushwacker" outfits in the area in 1862/63 including some of Stand Waites Indian Cavalry. T.R Livingstone reigned terror on his native county on several occasions. Sidney Jackman transited the area in '62 as did Coffee with his cavalry. Several irregular Union troops as well as regular CSA and USA troops transited the area using that road numerous times.
For a very good listing of OR listed actions supplemented where possible by other documentation I reccomend "The Timeline of the Civil War in Newton County" at http://freepages.history.rootsweb.ancestry.com/~cappscreek/civilwar/cwtimeline.html
It also backs into a very well done site on Barry County.
I've not found anything regarding the incident mentioned per se in Goodspeeds 1889 history. Most of the fighting appears to be recorded in the eastern portion of the county i.e. Neosho, Granby (site of lead mines), Jollification (also known as Jolly and before that Isbell Mills, Isbell being a significant slave holder prior to the war and pioneer settler of Newton Co.). These areas were where most of the southern leaning and slave owning farmers and merchants of Newton County lived and held property. I'll keep looking but I suspect that the incident you described likely happened as described and it will be by accident that a primary source document to support the family lore will be found. That is not to mean you should stop looking but will likely need to dig into diaries, muster books, county archives etc.