Bad faith is characterized by inauthenticity, meaning: acting or arguing in discordance with one's true beliefs or intentions.

Edit: bad faith is additionally characterized by its intentional stance, meaning that it shouldn't be confused with a state of ego dystonicity (wherein the actor acts compulsively against their self-perceived "true" nature).

To the best of my knowledge, there is no serious interpretation of Socrates in which his recorded expressions are considered to be in bad faith. The absolute closest stretch would be arguing that the Socratic method is in some sense "faithless," which is distinct from the negative nature of bad faith.