I've found your great-grandfather's birth entry in the register. I'll try and post a copy of it separately (it's not working trying to attach it to this at the moment). He was born in High Street, Dalbeattie on 3 August 1873, and his name is given as Robert Burns, though interestingly there's a note in the margin of "alteration of child's name" on 14 November 1873 which seems to say see the register of corrections (so don't know if it was changing his name from Robert to James or from Burns to Bott).
His mother's name is, of course, Agnes Burns, and it seems to say "domicil Creetown-Kirkmabreck" by her name, as well as giving her occupation as farm servant. No father's name given ("illegitimate").
His mother must be the Agnes Burns living at High Street, Dalbeattie on the 1871 census. Aged 25, born Creetown, occ. domestic servant. Also living there are her parents Hugh (aged 76) and Agnes (aged 66) Burns, both born in Ireland, and their grandson Robert Burns, 5, also born in Creetown (so must be either Agnes' son or her nephew).
This seems to fit with the Bott information (though she may not have been totally honest about her age!)
