First, if you have a choice, don't use VB6 which is a legacy environment. So if possible shift to VB.NET.
Secondly, Access is basically just a flat file so what you need is access to the file itself. You can map the share using both IP or UNC or use the file without mapping.
Thirdly, you didn't mention the technology you want to use. If you are really required to use VB6, I think ADO would be the logical choice. Here's one tutorial how to connect to an Access database with ODBC using ADO: http://www.vb6.us/tutorials/database-access-ado-vb6-tutorial