I have found much research that has been done for these two gentlemen, and much of it overlaps. Digging through the records, here is what I have discovered:
William Bell (b. 1740, Virginia) and Mary Foster (b. 1745, Virginia) had several children. Among them, were two sons:
Judge William Bell, Sr., born in 1768, Virginia
Married about 1786 to Sarah Knight, born in 1768, Virginia
Son, James M. Bell, born in 1815, Kentucky
Married in 1845 to Mary Ann Elizabeth Hall, born 1825, Kentucky
Thomas Bell, born in 1773, Virginia
Married about 1799 to Hannah Boggess, born in 1781, Kentucky
Son, James Montgomery Bell, born in 1812, Kentucky
Married in 1835 to Nancy G. Boggess, born in 1814, Kentucky
Much of the research that has been done suggests that James Montgomery Bell and James M. Bell are the same person, having married Nancy G. Boggess first, and then Mary Ann Elizabeth Hall, ten years later.
That assumption is false.
James M. Bell and Mary Ann Elizabeth Hall appear in the 1850, 1860, 1870, and 1880 US Census records, all in McCracken County, Kentucky.
Meanwhile, James Montgomery Bell and Nancy G. Boggess are listed in the 1840 and 1850 US Census Records in Muhlenberg County, Kentucky, and 1860 in Hopkins County, Kentucky.
The information listed in the 1850 and 1860 US Census Records proves that James M. Bell and James Montgomery Bell are not the same person.