The EmbeddedGraphDatabase class includes a convenience method to get instances of Neo4j management beans. The common JMX service can be used as well, but from your code you probably rather want to use the approach outlined here.

This example shows how to get the start time of a database:

private static Date getStartTimeFromManagementBean(
        GraphDatabaseService graphDbService )
{
    // use EmbeddedGraphDatabase to access management beans
    AbstractGraphDatabase graphDb = (AbstractGraphDatabase) graphDbService;
    Kernel kernel = graphDb.getSingleManagementBean( Kernel.class );
    Date startTime = kernel.getKernelStartTime();
    return startTime;
}

Depending on which Neo4j edition you are using different sets of management beans are available.

Full source code: JmxTest.java