ALL THAT I HAVE on the Bartholomew Alder/Elizabeth unknown line are:
1.) John Alder (12 Sep 1764 - aft 1832) married to a Mary KNIGHT Alder, John being born in Maryland, and dying in Marion Co, Tennessee, having had four children;

2.) An Unknown Alder married to a Henry Smith.

The Mingo Indians captured and raised Bartholomew's son (by Hannah Worthington), Johnathan. This is in the book by Nelson, Larry. A History of Jonathan Alder: His Captivity and Life with the Indians. (Akron, OH: University of Akron Press, 2002).

All the research I've done has been on-line for my half-sisters, so it's subject to revision. Best of luck with your lineage search.