SMS BAYERN was capable to make 23 kts, perhaps even touching 24 if forced to do this. But then again- it never was forced to overload conditions in her service time so we don´t know.
Or do we?
I tend to say-yes we can. At least we can approximate her top speed in within reasonably close margins owing to primary sources aviable through the Bundesarchiv.
Let me first examine what happened. As has been pointed out already, BAYERN, KÖNIG and GROßER KURFÜRST were attached to the 1st scouting group. However, the decision to do so is not explainable by the longer range of it´s guns or the experience to engage a QE in the run to the south. It was considered of utmost priority after Doggerbank that "Hipper´s scouting element should be a homogenious force with regard to speed for any future operation" (Pohl in his immediatvortrag).
We know that the two KÖNIG´s attached to his force were capable of 23 kts which is what qualified them for this purpose. There are only a few other Dreadnoughts recorded to be capable of this: SMS KAISER, which made 23.6 kts in her fastest trial run. To attach BAYERN with the 1st SG and not SMS KAISER instead would thus violate standing orders. The attachement of the BAYERN is only explainable in case the ship is capable of these high speeds if forced.
Now, let´s turn to the trial conditions before and after outbreak of hostilities. In peacetime, HSF ships used the construction depl. and max. possible overload to run the measured mile (You know that VON DER TANN forced it´s engines to 164% rated power to reach 28.124 kts in her peacetime trials, an incredible performance). Rated contract speed of VON DER TANN, f.e. was specified to be min. 24.8 kts for 6 hours continous, altough she handily exceeded that in her trials.
SMS KAISER also benefitted from making their trials completely under peacetime rules with her powerplant forced to even more horrible 178% of it´s rated power. The machinery was fully capable to deal with these extreme steam manifold pressures for a brief period of time. Needless to say that none of the KÖNIG´s or DERFFLINGER´s or BAYERN´s had this advantage. With the outbreak of hostilities, K-office changed the definition of mile runs towards so called "Kriegsmeilenfahrten" (war miles), which included a significantly increased deplacement (1/3 more crew and fuel and some more ammunition, too) and limited the poweroutput to ~120% permissable overload instead of the "as much as possible" practice used in peacetimes. Consequently DERFFLINGER made 28.0 kts in her trials at exactly 120% rated power, even though more speed would have been possible and the KÖNIG´s clocked in 22 kts at in between 130 and 140% power (they tricked a bit in that they raised the design poweroutput from 31,000 SHP to 36,000 SHP after these trials to make them "legal"), altough both classes were capable of much higher speeds.
SMS BAYERN clocked in 22.23 kts in her wartime trials at 116% rated power. The conditions of these trials -KÖNIG at the one hand and BAYERN at the other- are entirely comparable. This alone indicates that these ships were at least half a kt faster than the KÖNIGs and not slower in that they required much less overload for the same speed at identic load conditions (relative displacement). The powerplant of BAYERN was rated with 48,000 SHP (identic to that of VON DER TANN in this regard) and in peacetime would certainly have been forced to 70-80,000 SHP (as was VON DER TANN with 79,009 SHP) instead of the mere 55,900 SHP recorded in these trials. This made BAYERN the fastest Dreadnought in this period.
I happen to come across trial results of speed trials carried out withSMS BADEN dating to dec, 9th, 1916 to jan. 1917. These also assumed wartime trial conditions as evidenced by the displacement given below. The trial was run with anti-torpedonets (which later were removed, saving 48 ts) and with full wartime outfits & crews (note that BADEN was heavier and larger, beeing the fleet flagship from the start).
SMS BADEN, 9th, dec. 1916 (6 hours trials in 34/5m deep water):
6,208 SHP: 12.451 kts
13,130 SHP: 15.828 kts
24,978 SHP: 19.116 kts
37,430 SHP: 21.548 Kts
52,815 SHP: 22.301 kts
wind: ESE, force 3
draught before / after: 8.55m / 8.41m (=29,000 -28,500 ts, normal combat load)
SMS BADEN, 13th dec. 1916 (in 25m deep water):
13,024 SHP: 14.516 kts
22,935 SHP: 17.844 kts
38,569 SHP: 20.661 kts
54,756 SHP: 21.803 kts
wind: SSW, force 6
draught: 9.02m (30,780 ts max. war combat displacement)
SMS BADEN, 13th dec. 1916 (in 34/5 m deep water):
6,574 SHP: 11.982 kts
13,056 SHP: 15.095 kts
22,981 SHP: 18.250 kts
38,574 SHP: 20.931 kts
54,113 SHP: 22.086 kts
wind: SSW, force 6
draught: 9.02m (30,780 ts max. war combat displacement)
SMS BADEN, 6th Jan. 1917 (all 6 hour runs):
31,493 SHP: 19.755 kts (in 35m depth)
33,457 SHP: 20.371 kts (in 25m depth)
54,746 SHP: 21.801 kts (in 35m depth)
wind force: 5-6
draught: before trials: 9.01m; after trials: 8.95m (=avg. 30,500 ts -max. war combat displacement)
-note that BADEN only forced 110-113% rated power in miles which must be considered shallow for a 180m long hull and thus even higher speeds should be expected from her trials. The official commission in responsibility for BAYERN´s trials noted that the Eckernförde measured mile was way to shallow (25 & 35m) and that in between the range of critical speed v=18-25 kts a sudden increase of in between 15 to 25% of power was noticed than would have been possible in water with at least one half shiplength deepness (when these effects completely disappear). According to K-office calculations, the reduction in speed by wave effects caused by a to shallow measured mile as evidenced by the comparative tests carried out in 25m and 35m deep water, respectively would result in no less than 22.4 Kts at the recorded ca. 54,000 SHP in ca. 90m deep water and max. overload displacement with more than 23 kts achievable at normal combat displacement (the dec. 9th trial was calculated back to 22.8 kts at 52,815 SHP in 50m). It may be speculated that even higher speeds are well in within the realm of possibility given that the Seehahn company didn´t force the engines to even moderate overpower condition (e.g. 120% rated power) as did other contractors. This is obvious if You compare 6 hour trials with 1 hour runs, Seehahn found 110% beeing perfectly ok for both- By any standarts, there was no forced one hour trial done here!
If You ask me for my opinion or my 2 cents, here they come:
Check these figures from above carefully. F.e. the difference in displacement for a 35m deep trials from runs commenced at dec. 9th & 13th. This alone cut BADEN´s top down speed by approx. 0.7 to 0.8 kts at ca. 38,000 SHP. Thus, on dec. 13th, BADEN would be able to make 23 kts at 54,000 SHP had they used normal combat load, despite force 6 and shallow water. This power could be easily kept for 6 hours as we know from the january trials, it´s not even close to all out max. performance in good weather and a deep measured mile.
The Parson turbines had more capacity than those installed in either KAISER or KÖNIG class and the boilers had more steam generating capabilities as well and much more condenser reserves than those of the earlier Dreadnoughts. In peacetime, the powerplants would have been forced to a minimum of 150% output (that is: 72,000 SHP & more) and the much easier construction displacement would be used for the trials, which would easily generate speeds in excess of 24 kts even and may have been able to touch 25 kts under ideal trial conditions (that is deep water and heavy overload).