Hi Jared,
When you publish web services in ArcGIS Server, they are accessible publicly by default. So if your Server site is exposed to the internet, then you simply provide your customers with the Services Directory URL of the Server site. They should be able to access.
FYI, in my view - you may want to consider a mix or public and private web services. See this help topic,
Supporting a mix of public and private services—ArcGIS Server Administration (Windows) | ArcGIS Ente...
Hope this helps,
