Bridge is just another way to connect to your database.
Normally program uses direct MySQL connection to remote database installed at website or some other web server. In some cases this type of connection does not work - your hosting provider may not allow direct connections or your LAN settings/firewall prevent connection from being established. Bridge allows you to work with remote database with no direct MySQL connection established.

While working through bridge you must store your temporary data somewhere in database. Bridge is used only for two major operations - retrieve data from remote database and post data to that database. You must understand the difference between bridge connection and MySQL connection. Bridge is not a connection itself, actually this is just a way to transfer files between remote and local machine and nothing more. Do not use bridge connection in combination with direct MySQL connection on same store - it will not damage your data however will be very slow and uncomfortable.

See an example of bridge settings below. BTW those settings displayed in yellow area are valid - you may try them. Remember that it is osCommerce database so it will be incompatible with other Store Managers.

Retrieving data is very similar to restore operation of backup/restore wizard. Actually program posts a request to bridge.php file asking it to generate database backup (SQL) script. After script generated it will be transferred to Store Manager application and executed on database specified in "Store Database Settings" - your local (Embedded) database. After this operation you will get mirror copy of your remote (store) database on your local computer.

Select "Tools->Database Bridge->Get Data from Web" to retrieve script file. After script is executed you get complete copy of your remote store on yout local machine. You may work with the program now - all modifications one by one will be saved into one file. This file contains all SQL commands modifying your data such as DELETE, INSERT, UPDATE, ALTER and so on.

After all modifications you have to update your remote store with all changes done locally. Select "Tools->Database Bridge->Post Changes to Web". This action will post all stored commands to bridge.php installed on your store. After receiving file bridge will execute all commands one by one in order as they were stored. After all commands executed successfully your remote store will reflect all changes you made locally.