No it is not worth buying Barik Card
Yes, you save vs. single ride tickets
The Barik card is a prepaid, contactless, shareable, transport card for the province of Bizkaia which allows you to use all public transport including buses, metro, tram, and funicular in and around Bilbao. You can save almost 50% compared to buying single ride tickets that cost about 1.5 euros.
But only if you travel a lot
To get any advantage out of Barik card, you will have to stay longer at Bilbao and travel often by public transport.
Barik cannot be used beyond Bilbao
You will not be able to use Barik card in San Sebastian as it is in a different Basque province (Guipuzkoa) and Barik is only for Bizkaia. Still, the good thing with Barik is that you can use the Basque San Sebastian Euskotrain and you can also share the card with fellow travelers. Just make sure there is enough balance loaded on the card.
Hence, my recommendation that tourists need not buy Barik card.