I didn't find a way to tell the bureaucracy plugin to upload to the current namespace :rolleyes:.
I ended up using the upload plugin (
https://www.dokuwiki.org/plugin:upload) in addition. With this plugin, you can define the upload path as well and you can use keywords for things like the current namespace.
I ended up with the following one-liner in my template for bureaucracy action:
{{upload>@current@|RENAMEABLE}}
It works very well for me, but I need only upload functionality.