These potions last 30 min, are stackable but vanish if your character dies. Some are available through quests, but mostly they are purchased with Station Cash in the Marketplace.
Potion of Adventure I = 10% exp. bonus
Potion of Adventure II = 25% exp. bonus
Potion of Adventure III = 50% exp. bonus
The Marketplace purchased "Bottle(s) of Adventure" use the same exp. bonus scale, but last longer and persist through death. "Bottle(s) of Shared Adventure" simply extend the clicked effect on their entire group (if they have open buff slots and are in range).
As comparison the Veteran AA, "Lesson of the Devoted" gives 100% exp. bonus (double) for 30 min. and persists through death.
(List of Alla's adventure potion effects)