Are you talking about bore sighting only or bullet impact?

If only bore sighting, you will need to shoot it and see where the first barrel is impacting. There will be no guarantee that both barrels will regulate with a scope and mounts, unless it was regulated for that specific scope and mounts.

Bore sighting alone will only be so good, as the barrels will move to an extent while the bullet is still travelling in the barrels. The regulation will have allowed for this movement.

Bore sight it as you have done. Shoot that barrel bore sighted. I would guess it will not be on at all, so adjust the scope to close to the impact as with a single barrel rifle with as many shots as it takes. Then try the second barrel. ie shoot one shot from the first barrel, then one from the second barrel, and see how the two rounds go together. You may be lucky.

When discussing this with the gunmakers who regulate rifles at Heym and Verney-Carron both said the rifle needs to be setup either for open sights OR a scope. Of course we know some guys are lucky and their rifles seem to handle both.

Searcy could re-regulate the rifle for your scope and mounts now installed if needed.

Also you could try different loads and see if that has any influence.

If you plan to use open sights still, but have a QD scope option for longer shots, and the rifle does not regulate with the scope, a lesser alternative would be to sight ONE barrel for the scope. At least you know the one barrel will be spot on.