Bismarck was a major threat, because of what it could do, and what preventing that meant for the Royal Navy. She was a major threat to the Atlantic convoy routes that Britain was relying upon for much of its food, as well as steel and other strategic materials. In 1941, Britain would import 14.7 million tonnes of food, and 15 million tonnes of raw materials. Losses to shipping on these routes, mainly from U-boats, were high - 5 million tonnes would be lost in 1941 alone, and British shipbuilding couldn't replace this (see this chapter from British War Economy by Hancock and Gowing).

Bismarck represented a further threat to these routes, as she could wipe out any convoy she ran into if it wasn't escorted by a battleship. Other surface raiders, such as the cruiser Admiral Scheer and battlecruisers Scharnhorst and Gneisenau were greatly effective - Scheer would sink over 100,000 tonnes on a single cruise in 1940-41, while Scharnhorst and Gneisenau would sink a similar amount between them during Operation Berlin. There's little reason to believe that Bismarck wouldn't have been as capable. Of course, the RN could have escorted the convoys with battleships, and did as a matter of routine when German surface raiders were out. However, this took them away from areas where the Admiralty would have preferred them to be, such as the Mediterranean. It also exposed them to submarine attack. There was also the threat that Bismarck could join up with Scharnhorst and Gneisenau at Brest. There, they would form a force that the British couldn't effectively counter with additional convoy escorts, but would instead have to be hunted down, a far more difficult task.

For an example of what a single warship at large can do, check out the reign of terror of the German cruiser Emden in ww1.

It bombarded both coasts of India, shelling madras, and remained at large until it was sunk by hmas Sydney.

The very name Emden entered Usage into 4 languages (malayalam, Tamil , sinhala and Telugu) as a big guy, a dark guy, a scary guy, as a bold and daring piece. Mothers would scare their troublesome children into eating their food by telling them the Emden would take them away. Tens of thousands evacuated madras. Songs ( more akin to doggerel) were sung on the Emden, and on its destruction.

There is a recent post on /r/warshipporn with cites.

The British empire, let alone the British war effort was ultimately dependent on the maritime supply chain tying far flung lands together. A single warship could not overthrow this, but it could severely impact the overstretched supply vessels and bombard random areas, causing havoc.

/u/forthmaninaboat has summarized it well.

It also worth remembering that Churchill was concerned about shipping and refused to release that, which contributed to the death of millions in the Bengal famine. To give an idea of how important shipping lines can be