I was away, and then couldn't remember how to reply. The family would have been in USA by 1861 census, probably for 1851 for Martin Burns but maybe not for Bridget. Here is some basic information (Abbreviation: SPENCER= "town of Spencer near Cincinnati, Hamilton County, Ohio, USA" and GRASSCREEK= "town of Grass Creek, Wayne township, Fulton County, Indiana, USA".
Martin Burns, b. 15-Nov-1820 Northern Ireland, imm. about 1847 to USA, m. about 1855-1856 to Bridget G Flynn/Glynn, residence in 1860: SPENCER, moved to GRASSCREEK about 1865, d. 3-Mar-1877 of typhoid pneumonia, bur. St Anne Cemetery, GRASSCREEK.
Bridget G Flynn/Glynn, b. 15-Jan-1836 Turloughmore, Co Galway, Ireland (per her death certificate), daughter of James Flynn of Turloughmore and Margret Higgens of Turoughmore, d. 8-Sep-1904 GRASSCREEK. [Note another person's family tree states that she was born 21-Jun-1836 Tuam, Galway, but I do not know where they came up with this piece of data]
Children of Martin and Bridget Burns includes:
My ancestor John P Burns, b. Jun-1857 SPENCER, d. 20-Mar-1912 GRASSCREEK.
Mary Ann Burns, b. 9-Sep-1959 Cincinnati, Hamilton County, Ohio, USA, d. after 1923.
Margaret Burns, b. about 1864 SPENCER, d. after 1900.
Sarah Jane Burns, b. Oct-1866 GRASSCREEK, d. 1-Jan-1945.
Elizabeth Cecilia Burns, b. 2-Nov-1870 GRASSCREEK, d. 9-Aug-1908 Indiana, USA.
Female infant, b. 19-Jan-1871 GRASSCREEK, d. 27-Feb-1871 GRASSCREEK, bur. St Anne w/parents.
Julia A Burns, b. Apr-1873 GRASSCREEK, d. 1951 Logansport, Cass County, Indiana, USA.
Martin Burns Jr, b. 11-Sep-1875 GRASSCREEK, d. 8-Jul-1957 Kokomo, Howard County, Indiana, USA.
The family was in SPENCER in the 1860 US census, then in GRASSCREEK in the 1870, 1880, 1900 US censuses.
Thank you for any information that you find identifying where they come from in Ireland.