As someone with a B.A. in History who specialized in American history, I am well aware of the horrors associated with the slave trade.
My apology, like most of yours, will not mean much, as I have never owned a slave, nor (To the best of my knowledge) am I descended from anyone who owned slaves.
I also don't believe I should wallow in self- imposed guilt over something that happened centuries ago in which the only common factor between myself and the perpetrators is skin color.
However, I will say that I am very sorry that slavery happened, in much the same way that I am very sorry that other historical atrocities happened, such as the Holocaust and the campaigns of genocide against Native- Americans.