So far, when I had to connect to an 32-bit Access Database, I simply executed the application using 32-bit JVM. However, I am now developing an application that requires 64-
Now that the JDBC-ODBC Bridge has been removed from Java 8 all of these issues surrounding Access ODBC will increasingly become a thing of the past and a "real" JDBC driver will be required.
As mentioned in an earlier answer, UCanAccess is a free open-source option. It is a pure Java implementation that does not use ODBC at all, so it will work regardless of the platform (Windows, Linux, ...) or architecture (32-bit or 64-bit).
For more information on using UCanAccess, see the related question here.