Is it possible to transfer game data from one account to another on the same PS4?
I would like to transfer my progress in Bloodborne from my account to my Dad's account on the same PS4, and continue playing the game on my Dad's account. That's because I have registered myself as a child account though I am 16, and my Dad is the Family Manager. By doing so, I can play the game online through my Dad's account.
Is it possible to continue my current progress in another account on the same console?
No, you cannot do this because Bloodborne save files are bound to a PSN account.
I've just tried moving around my Bloodborne saves via usb copy method from this question: Copy game data from one PS4 to another? and my second account cannot see saves created by my main account.