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Your reading is correct - Bloodthirster never attacked the player it dealt damage to, so it may be declared as an attacker in the next combat.Comprehensive Rules wrote:508.4. If a creature is put onto the battlefield attacking, its controller chooses which defending player, planeswalker a defending player controls, or battle a defending player protects it's attacking as it enters the battlefield (unless the effect that put it onto the battlefield specifies what it's attacking). Similarly, if an effect states that a creature is attacking, its controller chooses which defending player, planeswalker a defending player controls, or battle a defending player protects it's attacking (unless the effect has already specified). Such creatures are "attacking" but, for the purposes of trigger events and effects, they never "attacked."