According to the Wikia for Once Upon a Time:
In the episode, the Queen says to Monte Cristo:
"The venom of the Agrabahn Viper. A bitter draught; slow and painful."
Obviously, the venom is poison. It is also, for the Queen, a solution or a medication to take care of her problem (whomever she is trying to kill).
In this quotation, the literal meaning is:
A measured portion of a liquid or aerosol medication; a dose.
a dose of liquid medicine
The phrase presumably comes from a line in Alexandre Dumas' book The Count of Monte Cristo:
"Hatred is blind, rage carries you away; and he who pours out vengeance runs the risk of tasting a bitter draught."
i.e. a person who seeks vengeance may receive harmful, unintended consequences.
In this quotation, the literal meaning is
a serving of drink (usually alcoholic) drawn from a keg
Bitter in this case meaning it has gone bad
Both definitions are related.
In any case, a bitter draught contextually means a harmful, imbibed substance.
As a title it can be interpreted as "a dastardly solution", or more literally as referring to the poison.