Take a look at org.bouncycastle.asn1.x500.X500NameStyle and its implementations.
X500NameStyle x500NameStyle = RFC4519Style.INSTANCE;
X500Name x500name = new JcaX509CertificateHolder( certificate ).getIssuer();
RDN[] rdns = x500name.getRDNs();
for ( RDN rdn : rdns ) {
for ( AttributeTypeAndValue attribute : rdn.getTypesAndValues() ) {
System.out.printf( "%s (%s) = %s%n",
x500NameStyle.oidToDisplayName( attribute.getType() ),
attribute.getType(),
attribute.getValue()
);
}
}