If Im not mistaken.
Dark sides cost per tick is equal to 60% of Dark sides cost to put on.
Dark sides tick and the MP regain tick happen simultaneously. If you're attacking and then stop and just auto attacking, I believe you can "unsync" it so that you'll be losing MP and gaining MP at seperate intervals, this shows Darksides actual cost which to my knowledge is 60%.

For the sake of discussion, Piety increases your MP total & MP regeneration rate. As such if they're operating in sync, Piety directly decreases the cost of Darkside. Which also means in a Party with Piety bonus (scholar) your Darksides are costing slightly less. Darkside can't be affected by external MP of bards so the only way to decrease the effect of its Degen is Piety. This may mean that going with a Scholar will allow more Dark arts over an extensive period of time and possibly be a DPS/threat boost as a result. All of a Drks mp costs are static.