Q: Can you use the Barcelona Card to go on the hop on hop off double-decker tourist buses?
A: The Barcelona Card only covers you for free transport on the Public Transport system. This includes the Metro, FGC, local buses, and the RENFE train in Zone 1. At the time of writing the Barcelona Card does not entitle you to a discount for buying a "Hop On Hop Off Tourist Bus" ticket by any of the tourist bus operators in Barcelona.
The Barcelona Hop on Hop of tourist buses will take you to many of the main attractions in Barcelona and you can use your Barcelona Card for either free entry into those attractions or discounted entry into the attraction depending on the offer at the time. However the Barcelona Card does not cover the cost for using a Barcelona tourist bus services itself.