Access is part of the Microsoft Office suite, which, I thought was available for mac.
Also, the application "Access" and the Microsoft Jet Database engine are often confused.
If you only need to read and write from a Jet database (.mdb file) you don't need to actually buy Access.
There is a odbc-jdbc bridge that ships with Java (or used to anyway, I haven't looked for it in a long time).
You would just need to install enough of Windows to create an ODBC entry.