For Bless Weapon, No
Any time a power lets you roll additional dice for damage not included with the normal attack and it DOES NOT refer to this damage as "Extra Damage", you add your modifiers again. In this instance you used bless weapon which specifically refers to the damage as "extra radiant damage" which makes it a part of the original attack in terms of rolling.
For example the bard power Echoing Weapon from Heroes of the Feywild adds damage to the next attack a weapon makes but this damage is not classified as "Extra Damage" because of this any bonuses that can be applied more than once per turn are applied a second time for that attack.
Encounter + Arcane, Thunder Minor Action Melee 1
Target: One weapon
Effect: Until the end of your next turn, the next
weapon attack made with the target weapon deals 2d6 thunder damage to
one target of the attack, regardless of whether the attack hits or
In comparison the Assassin's Strike power from Heroes of Shadow allows you to roll an extra 1d10 damage after you successfully hit a creature but this time the damage is referred to as "Extra Damage" and because of that the damage is considered to be part of the original attack and you only roll modifiers once.
Encounter Martial, No Action Personal
Special: Nothing but a short or extended rest can allow you to regain the use
of this power.
Trigger: You hit a creature within 5 squares of you
with an attack using a weapon.
Target: The creature you hit.
The target takes 1d10 extra damage from the triggering attack. If the
target is helpless, this damage is maximized.