If we use the timing as per PoW's salvo chart we get open fire:HOOD opened fire at approximately 0553 on May 24th, her course then being 300 degrees, range about 26500 yards. BISMARCK and PRINCE OF WALES opened fire very shortly afterwards. According to the statements from survivors of BISMARCK, PRINZ EUGEN also fired at HOOD over the BISMARCK (See C.B.4051(24) OF August 1941, page 14)...
Very shortly after 0555 a fire was observed somewhere on the port after end of the boat deck of HOOD. We consider it established that this fire was caused by a hit from BISMARCK's third salvo. It burned with a clear flame and appeared to spread and then die down. Just before 0600 V.A.C.B.S. hoisted a signal for a further turn of 20 degrees to port together, (the range at the time being about 16300 yards) but it was never executed as at 0600 HOOD blew up and sank in just under 3 minutes.
http://www.hmshood.org.uk/reference/off ... 9to144.htm
Bismark and PoW at 0553
So a fire on Hood at ~0555 caused by Bismarck's 3rd salvo, and from that Bismarck must have opened fire prior to 0555.