A rogue receives a bonus Cunning Action, and one option is to Dash. My understanding is a Dash allows a player to move up to twice his speed for his turn.
If a rogue is using a regular action to Dash (hence, is already dashing) can he also use his cunning action as a bonus to Dash again — effectively moving 4 times normal speed in a turn?
Cunning Action absolutely does let you Dash again, but Dash doesn't work quite like you're remembering (PHB, p. 192):
When you take the Dash action, you gain extra movement for the current turn. The increase equals your speed, after applying any modifiers.
Speed and movement are separate concepts in 5e. Usually your allowed movement for the turn = your speed. Dash doesn't multiply or change your speed, it makes your movement this turn = your speed + your speed.
With only one Dash, speed + speed ends up the same as speed × 2, but with two Dashes the difference matters, since movement = speed + speed + speed does not equal speed × 4, but equals instead speed × 3.
So yes, you can do this. But you don't move four times your speed, you only move thrice your speed.
