Aside from using water from the soil, roots also absorb nutrients that the plant needs in order to grow. Of course, the soil provided to the bonsai is very little and thus the nutrients that may have been contained in it to begin with will be exhausted fairly quickly. To ensure that your bonsai responds well to styling, heals well and is pest resistant you will need to provide the food that it needs.
The danger when using chemical fertilizers is that it is possible to overdose the plant and cause root burn or other harm. However by simply following the directions of the package or even diluting the fertilizer further you can easily avoid this.
Organic fertilizers, as the name suggests, are generally made exclusively from organic sources such as kelp, fishmeal, chicken manure and more. However several organic fertilizers are now being fortified chemically with trace elements or other nutrients, which are difficult to find in sufficient quantity, organically.
Unlike chemical fertilizer it is virtually impossible to overdose with organic fertilizers. The reason for this is that generally they are not as concentrated.