Read Bright Veil carefully. It actually does specify how long it lasts for. Bright Veil reads "As long as this Pokemon is your Active Pokemon, whenever your opponent plays an Item card from his or her hand, prevent all effects of that card done to your Pokemon.
Bright Veil only activates the instant the card is played from your hand. At any other time during either player's turn, Bright Veil does not activate, because it is not "when your opponent plays an Item card from his or her hand". Instead it is when your opponent is attacking.
Think of it as a two-step process. Step 1 is when you play the item card from your hand. Step 2 is when your pokemon attacks. Due to Bright Veil's extremely specific wording of when the item card is played from your opponent's hand, it can only activate during Step 1. During Step 2, when G-Booster is being used to attack, it is too late for Bright Veil to activate.