In short
No direct link from Heraklion. First Heraklion → Sitia (4-7 buses/day, ~3h, ~€16), then Sitia → Vai, seasonal and very limited (~1h, ~€4), with a sometimes non-existent weekend return. Our verdict: not advised as a day trip from Heraklion — better to sleep in Sitia, or rent a car (25 km, ~35 min from Sitia).