The Bismark's limited escorts was not uncommon for surface raiders. It was common since the Age of Sail for large combatants to sail independently without escorts who would require logistics support along the way. In some ways, traveling alone was an advantage, especially in waters like the south Atlantic where the Bismark was unlikely to see enemy submarines. But the reality was that the big ships were vulnerable to naval air power and submarines. The quick sinking of the HMS Hood came as a great shock to the British people and gave root to the fear that the UK might lose the war. Churchill, therefore, made sinking the Bismark a priority, sending a massive force to defeat it. A few destroyers or cruiser escorts probably would not have made much difference at that point.

Bismark's lack of escort ships had much to do with the German Navy's shift in strategy that emphasized submarines over big surface ships.

In many ways, the shift to submarines -- made after a spending spree on battleships and cruisers during the 1930s -- made sense if the mission of the Navy was to be denial of access to British merchant ships, the same strategy Germany used in World War I. As an anti-access weapon, the submarine is ideal. It can be built quickly and cheaply and were deadly against unescorted merchant vessels. So through 1943, the German Navy's large submarine service and battleships like the Bismark, forced allied forces to assign destroyers and battleships (and later small aircraft carriers) to protect convoys.

Production of submarines, almost exclusively by the end of the war, also made sense because it demanded less steel from German industry than the Army and Air Force.

The shift to submarine construction, however, deprived the Navy of the ability to support an amphibious assault against the United Kingdom. Navy chief, Admiral Erich Raeder, had never considered that invasion would be Germany's goal and had not constructed the Navy with that goal. Moreover, the UK's breaking of Germany's submarine codes, the development of sonar, airborne radar, and radio detection techniques ("Huff-Duff"), turned the tables on the submarines, too.

The unanswered question is why the Bismarck received no support as she sailed round in circles - was there a failure to communicate or was there no support available or was it decided to leave her to her fate?

The German navy was the weakest part in Germany and Hitler decided to built it as last chance to defeat the Royal Navy. The biggest battleship ever built by Germany was escorted by the largest available "second" ship, a new heavy cruiser. Once was ready its mission was to destroy the British merchant fleet. A UK admiral was advised about German plans so he decided to make a duel of battleships in the Straits of Denmark.

The Bismark battleship was enough to win that duel because was only two ships against two. However, the Royal Navy was far from accept the defeat and decided to persecute with a small fleet (1 aircraft carrier and several battleships, a cruiser and destroyers). So, in that moment the Bismarck was totally surplused and its defeat was normal.

It was a great try by Germany but was a great mistake because the Royal Navy was the biggest of Europe. Only finishing the Z plan was able to defy the UK, a plan that hitler decided not to complete.

The Kriegsmarine had been following Plan Z with the outbreak of war predicted as 1945 not 1939 and at least 2 aircraft carriers were considered but only one the Graf Zeppelin was built and this was heavily damaged by an RAF air attack and not completed, 2 battleships and 2 battle-cruisers were also due to be constructed after the Tirpitz but the materials and men were turned over to U-Boat construction instead. Escorting the Bismarck with light cruisers and/or destroyers was not possible due to their short range, the Royal Navy had bases in the UK, Iceland, Canada, Gibraltar etc. and their ships were designed to protect the empire so range was a major consideration in their design.

Air power at sea was still unproven in May 1941 indeed the Prince of Wales was the first battleship to be sunk at sea by aircraft when the Japanese sank her in December 1941. Before then aircraft were considered as a means to find the enemy and guide ships to them, destroying them was not considered.

The operation that the Bismarck undertook was meant to include a meeting with the Scharnhorst and Gneisenau but the Scharnhorst was suffering from faulty boilers and her sister ship had been bombed and torpedoed in the harbor at Brest in France, Lutjens wanted to postpone the mission and wait for Tirpitz to complete her working up but was over ruled by Raeder the C-in-C of the German Navy.

As for the Prinz Eugen adding her Anti-aircraft armament as an escort it is interesting to note that none of the attacking Swordfish bi-planes were shot down in either attack despite the crew of the Bismarck receiving plenty of notice of the impending attacks but later examination of the German anti aircraft systems shows that they were calibrated to allow for a much faster aircraft, the Swordfish at top speed could officially manage 140 mph but due to the weather conditions encountered 85 mph was probably more accurate (I had the honor of knowing the pilot of one of the Swordfish that flew from HMS Victorious against the Bismarck and own a copy of his book). The German gunners allowed to much deflection!

As far as "battleships" go, the Germans only had the Bismarck. The Tirpitz had just completed construction and wasn't quite "ready" for major duty, and the battle-cruisers Scharnhorst and Gneisenau were undergoing repairs.

A more interesting question is why didn't Germany send out cruisers and destroyers with the Bismarck to protect it from "cheap shots." Apparently, no one felt that they were needed. The Bismarck originally had a cruiser escort, the Prinz Eugen, that did a great job of shielding the Bismarck against the opening fire of the Hood. But Bismarck's Admiral Luetgens apparently didn't feel the need for such an escort, and detached the Prinz Eugen for "independent" duty. The idea was that the Prinz Eugen could do more damage by itself than by accompanying a Bismarck that was damaged, and needed to head to port for repairs.

With benefit of hindsight, the Prinz Eugen's anti-aircraft fire might have helped save the Bismarck from air attack by the bombers of Britain's Ark Royal. But that's with hindsight, because no one thought in those terms at the time.

As identified in the first paragraph of the question, the purpose of Operation Rheinübung was a continuation of the commerce raids on allied shipping in the Atlantic. The Scharnhorst and Gneisenau had previously performed a similar exercise with great success.

Commerce raiding was a common tactic used against a superior (or simply numerically larger) naval force. It allowed the smaller force to do disproportionate damage against the enemy shipping while avoiding the risk of putting all of their warships at risk at once. By keeping their own ships dispersed, the Germans would force the British to spread their own forces to find and attack them. In that situation, there was the possibility that the German battleship would be able to out-fight the force it encountered (or simply out-run, as was the case when the Scharnhorst and Gneisenau encountered a couple of British battleships).

Had the Germans committed a larger flotilla (or even fleet) to the operation, it would have allowed the British to concentrate their forces too. In a fleet action the Germans would have, almost certainly, been outnumbered and outgunned. In which, case they would have been at risk of losing a considerable part of their surface fleet in a single action.