It was quite common years ago for schools and universities to have human skeletons for their studies, which were sourced through scientific suppliers. We are not aware of each school system’s policies for dealing with the ethical disposal of human skeletal remains, however, there does need to be legal and ethical consideration given when disposing of these and they should be treated with respect. Each state/territory has legislation regarding the use and disposal of human tissue and remains.
The human anatomy departments of universities, particularly those which have schools of medicine, are sometimes willing to accept donations of human skeletal remains from other teaching institutions, including schools. They are familiar with and governed by the state/territory legislation that applies in their jurisdiction. Other options include contacting medical waste disposal specialist companies who will dispose of human skeletal remains as medical waste.
However as your remains are now ashes, it may be helpful to contact your local government crematorium services for local advice. It appears that there is no legislation concerning these. They can be buried in a cemetery, kept in an urn or container or scattered on land or water. Please be aware that if you choose to spread the ashes, you may require permission from the land owners, or authorities, e.g. such as the local council, responsible for that land or water.
Here are some links to some interesting related articles:
‘All About Cremation Ashes’, Cremation solutions Inc. website, https://www.cremationsolutions.com/information/scattering-ashes/all-about-cremation-ashes/ (Accessed March 2016)
Australian National University, Policy: Collection, storage and disposal of human tissue in research, ANU Policy Library website, https://policies.anu.edu.au/cs/groups/confidential/@rs/documents/edrms/dxbf/mdaw/~edisp/anup_000394.pdf (Accessed March 2016)
‘Cremation ashes’, Fact sheet, NSW Government Health website, http://www.health.nsw.gov.au/environment/factsheets/Pages/cremation-ashes.aspx (April 2013)
Tasmanian Association for Hospice and Palliative Care. 2015. Our Final footprint: Dying simply and sustainably in Tasmania https://www.google.com.au/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=r... (Accessed March 2016)
UK Department for Culture, Media and Sport. 2005. Guidance for the Care of Human Remains in Museums. https://www.britishmuseum.org/pdf/DCMS%20Guide.pdf (Accessed March 2016)