We know now that Genetic material is passed over from one generation to the next, and blood, of course, is a reflection of that fact. Before that knowledge was common though, why was 'bloodline' the basis of determining handover of power or wealth from one generation to another? Even 'purity of bloodline' was a major factor in determining transfer of power.
I mean, it might as well have been last name, clan name, simple family tree or even hair color. Why blood, of all things, especially when the genetic factor was unknown?
Even without the formalities of genetics science, heredity has been broadly understood no doubt since pre-history, since the biomechanics of reproduction, and the presence of familial traits are pretty obvious. "Bloodline" refers not specifically to blood, but more generally to having the same blood/body, that is, being in the same family.