I have a local git repository with an already set up git origin.
Now the client is asking to have the project stored in their internal svn repository.
I'd like to keep the current git infrastructure for the development and to push to the svn server only some branches (eg. release branch).
Is git-svn bridge the correct solution in this case?
Yes, git-svn is a perfectly valid option for your case. You may do a git svn init ... on the existing git repository or do git svn clone to a new repository, adding your true origin later as git remote add origin ....
Git-svn will not really be an remote (like origin) for you, you will be using git svn xxx commands, most notably git svn rebase, git svn dcommit. The svn branch git svn dcommit would push to can be examined with git svn info.