How to convert BED to GFF3
Galaxy has API and API-consuming libraries (such as BioBlend) that will allow you to interactively script against it without opening the graphical interface at all.

However you can also take almost any tool out of Galaxy and use it independently since everything is open source. The converter you mentioned is available as a Python script here and the tool 'wrapper' which you can use to understand how to invoke the python script is next to it.