Upvote:5
If you take the route Google suggested at the moment (involving only funicular from Vallvidrera Inferior to Superior, then taking 111), you can use the Hola Barcelona Card.
The Hola Barcelona card includes public transport within Zone 1 (https://doc.atm.cat/ca/xarxa_ferrov_global.pdf), in which Tibidabo stop is situated.
Note though the Vallvidrera Funicular is included in the network, but the Tibidabo Funicular is not.