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I have my naya deck playing against a jund deck. I'm atking with my creature 3/3 and my opponent declares no blockers on the atking creatures and asked me "I'm not blocking, are you dealing the damage now?" I have a ghor-clan rampager in my hand and enough mana to bloodrush it but I'm not going to waste it unless he is blocking so I said "yes, I'm dealing 3 damage to you" and then he casted the searing spear on my 3/3. And then I said "in response, I'll bloodrush 4/4 and trample into my 3/3" but he said the question he asked makes himself to have the priority and I cannot do the bloodrush afterwards. Is that true??
You certainly can Bloodrush while the Searing Spear is on the stack. Nothing resolves on the stack or moves to the next phase of the turn without 'both' players passing priority.
Again, Bloodrush is an activated ability; and unless otherwise stated in the effect, all activated abilities are instant-speed.