Before the pull
Depending on the strat your raid use, the melees and hunters may be out of line of sight. If that's the case, you'll need a priest assigned to dispell them.
Other than that, there is nothing to assign: only one tank and every priests should be dispelling who they can.
You just need to take 2 or 3 Hourglass Sands that drops off the BWL trash. You'll use them when you have the Brood Affliction: Bronze debuff.
The fight
Your priority will be to dispell the Brood affliction: Blue and Brood affliction: Red off the raid.
When there is nothing to dispell, you'll be healing tank. That's nearly the only source of damages.
You should save your mana and CDs (Power infusion) for the Enrage of the boss. This will happen when the boss have 20% HP left. The tank will be taking loads of damages during this phase. If you have enough mana, you should spam a high rank of flash heal on tank during this phase.