I think I figured this out. I deleted everything in the bode plot except for one "line" to keep things simple, then did the following. I don't understand the advantage of having a parent hggroup object for the line object, but at least I can access the xdata and ydata.
hg = findobj('type', 'hggroup'); % Just one is found
ch = get(hg, 'children'); % Just one child, and its type is line
xd = get(ch, 'xdata');
yd = get(ch, 'ydata');
plot(xd, yd, 'r'); % Reproduces the "line" in the bode plot