When Asura Priest, which is equipped with Big Bang Shot, returns to my hand, is it removed from play?

Nope.........

Big Bang Shot
Increase the ATK of a monster equipped with this card by 400 points. When the equipped monster attacks with an ATK that is higher than the DEF of a Defense Position monster, inflict the difference as Battle Damage to your opponent's Life Points. When this card is removed from the field, remove the equipped monster from play.

Big Bang Shot must be removed from the field BEFORE the monster returns to your hand..... in your case it is the monster which is removed from the field...

no because asura priest is revome from the field and gone to your hand but big bang shot said wen this card is remove from the field remove the eguip monster from play.so if asura priest is remove from the thr field befor big bang shot so asura priest stay in your hand.

Note that "Big Bang Shot" will lose its target and destroy itself due to the game mechanics.