Hi!
As you may know, Abraham had three wives: Sarah, Hagar, and Keturah.
It's my understanding that Baha'u'llah was descended from Abraham through both Sarah and Keturah, and that the line from Sarah included David as well (though I don't know at what point before Jesus it then split off).
(And as a slight aside, the Bab, Baha'u'llah's forerunner, was a descendant of Hagar via Muhammad, so all three Abrahamic lines are represented in the Central Figures of the Baha'i Faith. Indeed, Shoghi Effendi was descended from both the Bab and Baha'u'llah, and was hence descended from _all three_ of Abraham's wives!)
So anyway, the short answer is that yes, Baha'u'llah was a descendant of David.
Best,
Bruce