I think, I previously misunderstood this message. It was asking about the salvo exchange and not about Bismarck's rudder failure. Sorry about that.
According to ADM 234-509: H.M.S. Suffolk Operations 23-26 May 1941
http://www.hmshood.org.uk/reference/off ... 9suff.html
, the Suffolk sighted Bismarck followed by Prinz Eugen at 1922 hours. There is no mention of firing from any side until 2031, when Bismarck is reported to have opened fire.
According to ADM 234-509: H.M.S. Norfolk's Gunnery and R.D.F. During Operations Against "Bismarck"
http://www.hmshood.org.uk/reference/off ... 9norf.html
, Norfolk was fired upon by the 8-inch cruiser (the Prinz Eugen) and splinters hit "X" Turret. But I suspect however that the "8-inch cruiser" referred above was actually Bismarck since I have not found any German official report or account metioning Prinz Eugen firing on 23 May, and it is well known that Bismarck fired on Norfolk and splinters fell aboard this cruiser.
Then we have Prinz Eugen and Bismarck's war diaries:
1922 / 1922 hours
Alarm from Bismarck: In direction 340º lateral direction [azimuth] is a shadow. Distance 130 hectometers [13,000 meters]. It is apparently an auxiliary cruiser which disappears immediately into the mist again. Formation is [obviously] being reported by him. Bismarck opens fire (about 5 volleys) and signals to the formation JD [Fire permission code Jot Dora “Open Fire!"]. Prinz Eugen has no target. By radar rangefinder II position finding reveals that [we are] dealing with a heavy cruiser running at 27-28 knots, course 195º, since massive superstructures and 3 stacks were observed at the first visual sighting.
2044 / 2044 hours-
The heavy cruiser comes into view at port astern at 206° azimuth, and opens fire on Prinz Eugen. [Underlined by hand by Brinkmann. UR]. The formation goes to flank speed. Prinz Eugen positions himself according to Fleet order in front of Bismarck. While picking up steam to starboard of Bismarck, Bismarck has rudder failure. Rudder position is starboard. Prinz Eugen is able to extract himself from closing further by 40° hard full rudder (which, as a rule, is not allowed at this high speed).
According to the KTB entry above the Prinz Eugen came under fire, but again I've never found a British official report or account that mentions Suffolk or Norfolk firing on 23 May.
I think that most probably the only ship that opened fired that afternoon/evening was the Bismarck at 2030 hours. Grenfell, Kennedy, Müllenheim-Rechberg, and others authors agree in that, and do not mention any of the other cruisers firing.