At least by the rules as they are written the dueling bonus applies to both attacks. On page 24 of the SRD the Dueling Fighting Style text is “When you are wielding a melee weapon in one hand and, no other weapons you gain a +2 bonus to damage rolls with that weapon.” Note that the bonus to damage is activated immediately. , so if you lose one of your psychic blades and immediately gain another you get that bonus applied.

At least by the rules as they are written the dueling bonus applies to both attacks. On page 24 of the SRD the Dueling Fighting Style text is:

When you are wielding a melee weapon in one hand and, no other weapons you gain a +2 bonus to damage rolls with that weapon.

Note that the bonus to damage is activated immediately. So, if you lose one of your psychic blades and immediately gain another you get that bonus applied.

There is a weapon in one hand at both times that dueling is used so you get the damage bonus.

At least by the rules as they are written the dueling bonus applies to both attacks. On page 24 of the SRD the Dueling Fighting Style text is “When you are wielding a melee weapon in one hand and, no other weapons you gain a +2 bonus to damage rolls with that weapon.” Note that the bonus to damage is activated immediately. , so if you lose one of your psychic blades and immediately gain another you get that bonus applied.