No. Part of the effect of the card is to choose X BB and another part of the
effect is that each of the chosen BB must burn a blood.
When you play WoC, you declare X, and you declare the X BB you are choosing
(along with declaring the rest of the effect of the card: that the BB will burn
blood, that the acting BB will get +x bleed).
> So if Veil of Darkness cancels it, I assume you do not
> get your blood back because it was not a cost?
If the card is canceled, then the effect is not applied.
The X BB are not chosen and they do not burn any blood.