The Damage Roll is the result of all the Damage Dice
You only apply your proficiency bonus from the Hexblade Curse once when calculating your damage from an attack.
Damage Rolls vs Damage Dice
The key here is in differentiating Damage Roll (the total for an attack) vs Damage Dice (individual rolls) when determining how to apply these effects.
The following logic then applies:
Hex is active on a target(PHB, 251)
you deal an extra 1d6 necrotic damage to the target whenever you hit it with an attack
Bestow Curse is active on a target(fifth level + to remove concentration) (PHB, 218)
your attacks and spells deal an extra 1d8 necrotic damage to the target.
Apply Hexblade Curse (XGtE, 55)
You gain a bonus to damage rolls against the cursed target. The bonus equals your proficiency bonus.
Your own Weapon (whatever it may be)
That gives you the following sets of damage rolls:
Bestow Curse Damage
The question now is in whether or not these are all separate damage rolls if it is a single damage roll.
Let's look at the Concentration mechanic
We can look at how keeping a concentration up works in conjunction with this.
We know that each separate damage roll from each source of damage (PHB, 203)
You make a separate saving throw for each source of damage
The attack is your source of damage, and all of the bits of that single attack comprise the damage. This would be the same if looking at a standard attack + hunter's mark. You have your total damage which are the damage dice AND the Hunter's Mark die. Only separately rolled attacks, or attacks that are separate like Magic Missile, are considered separate sources of damage.
This is supported by the PHB (196) under Damgage Rolls:
Each weapon, spell, and harmful monster ability specifies the damage it deals. You roll the damage die or dice, add any modifiers, and apply the damage to
your target. Magic weapons, special abilities, and other factors can grant a bonus to damage.
Damage Dice are a separate mechanic as seen by the use of the Fighting Style Great Weapon Fighter which specifically calls out the Dice rather than the roll:
When you roll a 1 or 2 on a damage die...
The language around Hexblade Curse is about Damage Rolls, not damage die. The curse therefore doesn't apply to individual dice or to each separate roll within a damage calculation.
That leaves you with you the following damage calculation:
Weapon Di(c)e + 1d6(hex necrotic)+1d8(BC necrotic) + Proficiency Bonus(Hexblade Curse)
There is only ONE Proficiency use per roll
Both the PHB (12) and Xanathar's (5) reference the following rule (emphasis mine):
Your proficiency bonus can’t be added to a single die roll or other number more than once.
This further substantiates that on your Damage Roll for the attack, you can't apply your Proficiency to each damage die.