In asexual organisms variation can occur from a variety of sources - mutations, homologous recombination and plasmid transfer. Mutations occur at a rate of roughly one base per million, meaning you would get between 0.1 and 10 in bacteria due to the size of their genomes.
In sexually reproducing organisms there are mutations and the crossing of gametes. The mutations occur in a near identical way to in asexual reproducing organisms as long as they occur in germline cells.
Asexually reproducing organisms reproduce much, much faster and so variation can occur more rapidly. For example the variation in the HIV viral propulation in an individual after 5 years is an immense diversity, higher than all the diversity that the human population has managed in thousands of years.