The cave is only worth photographing when the sun is high enough to reach that underwater opening, which in practice means roughly 11:00 to 13:00, on a clear day, with a calm sea. Earlier and later the chamber is still blue, but it is a dimmer, greyer blue, and it does not survive a phone camera.
This is why the day is long. Boats leave Hvar in the morning, cross to Biševo, and time their arrival at the entrance for the middle of the day — which also means every other boat in Dalmatia is doing the same thing. In July and August expect to wait at the tender boats, sometimes over an hour, floating in the sun.
The second variable is the sea. The entrance is low and open to the swell, so the cave closes whenever the water is not calm, sometimes at an hour’s notice. Trips are cancelled and rescheduled all season, and that is not the operator being difficult — it is the harbourmaster.
One more thing about the light: it does not photograph the way you see it. The chamber is dim, the tender is moving and automatic exposure turns that blue into grey. Turn the flash off — it kills the effect entirely — brace the phone against the side of the boat and shoot the water rather than the walls. Most people take twenty pictures and keep one. Look at it with your eyes first; fifteen minutes is not long.