Ten-to-one, "M.C." is Mary Curd.

1.  Jordan R. Dodd, ed.  1993.  Kentucky Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):

Bradshaw, Alexander

Campbell, Jane Frances

Aug 25, 1836

Mercer Co.

2.  1840 Census Index/Images (online at Ancestry.com; Image #33-34 of 98 — mis-indexed "Modshaw"; extracted by Diana Gale Matthiesen):

1840

KY

Christian Co.

pp. 205B-206A

Ln. 22

Alexander Bradshaw

100 010 - 100 010

020000-120010

0500000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 white male	4 or under	1835-1840	= J.E. (b. 1840) or ?
1 white male	20-29	1810-1820	= Alexander (b. 1814/5)
1 white female	4 or under	1835-1840	= M.C. (b. 1837/8)
1 white female	20-29	1810-1820	= Jane (b. 1814/5)
2 male slaves	10-23	1816-1830	= ?
1 female slave	9 or under	1830-1840	= ?
2 female slaves	10-23	1816-1830	= ?
1 female slave	55-99	1740-1784	= ?
5	persons employed in agriculture

If J.E. was born in 1841, then there is another son, born in 1840, who died before 1850.

3.  1850 Census Index/Images (online at Ancestry.com; Image #9 of 119):  District No. 2, Christian Co., KY, pp. 364A-364B, 71/73, enumerated 10 Aug 1850 (extracted by Diana Gale Matthiesen):

Alexander Bradshaw	35	M	Farmer	5,250	Kentucky
J.F.         "	35	F			"
M.C. Bradshaw	12	F			Kentucky
J.E. Bradshaw	9	M			"
L. Bradshaw	7	M			"
Susan J. Bradshaw	5	F			"
T. Bradshaw	1	M			"

Listed eight households from Alexander's sister, Orra (BRADSHAW) KELLY, who is listed next to their uncle, Capt. Benjamin BRADSHAW. 

4.  1860

5.  1870

6.  LDS.  Family Search: Census Records: 1880 United States (online at FamilySearch.org):

Census Place: 2nd Ward, Kansas City, Jackson, Missouri
Source: FHL Film #1254692; NARA Film #T9-0692; Pg 116B
	Relation	Sex	Marr	Race	Age	Birthplace	Occupation	Fa	Mo
Alexander BRADSHAW	Self	M	M	W	66	KY		VA	VA
Jane F. BRADSHAW	Wife	F	M	W	65	KY	Kpng Hse	VA	KY

7.  Messages in the Bradshaw Family Genealogy Forum (online at GenForum.com).

8.  Messages in the Campbell Family Genealogy Forum (online at GenForum.com).