Is it possible to use bulk upload in Safari or in firefox? If no, is it possible extend EpiServer File browser functionality?
No, the bulk upload in Internet Explorer is implemented as an ActiveX component, which is technology only supported by Internet Explorer.
Have you tried the WebDAV support? WebDAV in EPiServer CMS 5
Unfortunately it can be a bit tricky to configure on Windows clients, but I believe it should be fairly straight forward to get it working on MacOS.