This makes TestLink configuration different. As you can see at the steps indicated by Beltran, with:
it is assumed that both applications are in the same machine. So, you have to change that and create an user on the MySQL at Mantis machine to allow Testlink to acess remotely. To do so, first, change the config.inc.php with (MANTIS_MACHINE_IP must be substituted with the correct value):
Also, notice that the dbuser has changed. Now, go to the Mantis machine and create this user (TESTLINK_MACHINE_IP must be substituted with the correct value). The password used during the installation is needed.
mysql -uroot -p -e "CREATE USER 'mantis_testlink'@'TESTLINK_MACHINE_IP' IDENTIFIED BY 'yyyyyy'; GRANT ALL PRIVILEGES ON bitnami_mantis.* to 'mantis_testlink'@'TESTLINK_MACHINE_IP'; FLUSH PRIVILEGES;"
I hope it helps.