The general explanation that I'm aware of for the causes of the war is that Kaiser Wilhelm II, after taking power, got rid of Bismarck and decided to follow an agressive foreign policy: he began to pursue his colonial ambitions and expanding his navy (eventually threatening the UK), allowed Germany to alienate from the alliances that Bismarck had made with the UK and Russia, and allowed France to ally with them. The eventual spark was the assassination of austrian Archduke Frank Ferdinand, with Germany backing a military action against Serbia.
From this explanation, I'm led to believe that the war happened precisely because of Kaiser Wilhelm's ambitions. The questions I have are: what am I missing, and, if Bismarck's policies continued to be followed, would a war in such a scale still be a possibility?
Leaving aside the question of specific policies, Wilhelm II was not actually an autocratic ruler whose personal decisions informed every aspect of German policy. While Germany was not a constitutional monarchy a la the UK, it also wasn't an autocracy like Russia. While Wilhelm did have some influence, especially on military matters, there were major areas of German foreign policy that took place despite, rather than because of, his preferences. (For example, he was very unhappy with Germany's position on the Morocco crisis). So even if you feel that German policy was the cause of World War I, it isn't fair to lay it at the feet of Wilhelm himself.
As an aside, there was no UK-Germany alliance under Bismarck.
Source: Christopher Clark, 'Kaiser Wilhelm II: A Life in Power'