My thesis involves extraction of carbon from sugarcane bagasse through pyrolysis. The carbon extracted will be graphitized and consequently be synthesized as graphene oxide.
The ash in most recently harvested biomass contains a significant portion of water-soluble material, primarily alkali metals. However, in my experience, bagasse ash has very little of this, presumably because the water used to extract the sugar also dissolves the ash fraction. The remaining ash can be extracted with acids, though it is probably dominated by Si, in which case a very strong acid (HF, for example) will be required. Alternatively, this silica will be intimately bound in the bagasse and therefore the char. If you pulverize the material, it will have a significantly higher density than the char and could probably be gravimetrically separated.
Both of these processes will be expensive, both operationally and in capital investment. They also involve significant safety and environmental hazards. You may want to consider if it is worth it as there are much more pure biomass source materials available. For example, heartwood from trees (or sawdust) generally contains 0.1% ash, sometimes less. This is much lower than bagasse.
Just to add, ashes can also be removed or lowered by pretreatment of the biomass. This typically involves "washing" the biomass before pyrolysis or thermal conversion. For this process, distilled water will suffice as opposed to the use of chemicals which makes the process more environmentally friendly. Hope this helps.