Small size means that bacteria can reproduce quickly-- it is easy to make many small and simple cells in a short time. That rapidity means that errors are more likely to occur, increasing genetic diversity, as is also true when there are many, many individuals. Large populations offer more chances for mutation to have occurred even if DNA is carefully copied.
Work Step by Step
Think about this using two analogies: 1) Which can you make more quickly, lots of tiny crackers (just salt+water, mix and bake, like prokaryotic cells) or lots of big Spanish omelettes (eggs, cheese, vegetables, fussy cooking technique etc., like eukaryotic cells); 2) When are you more likely to make an error in your writing (like DNA copying), while working quickly under pressure or working slowly in a relaxed environment? Also consider population size. The larger a population, the more chances there are for there to be mutations within that population out of sheer probability. Every new replication is another roll of the dice on the development of one or many new mutations.