No, I haven't found a birth for Bridget, or a marriage for Margaret.
I'm assuming (probably a mistake!

) that as Bridget is William Gallagher's stepdaughter, and Thomas names a Margaret as his grandmother on his army records, that Margaret must have been previously married to a Keegan, thus having a daughter Bridget Keegan. William Gallagher being Margaret's second husband. The complicated family dynamics are not helping!
Bridget names her father as William Keegan on her marriage registration. She was born in 1872, so was only 16 when Thomas was born. I'm surprised she was allowed to keep the baby.
Bridget says she was born in Sligo, but as I've found that many offsprings' birth places on census are the same as the parents' birth places, whether the offspring were actually born there or not, I'm not taking that as gospel.