Effective method for waterproofing a tube through a hole drilled in the side of a bucket?
What you want is called a bulkhead fitting.

 

This has a gasket to make a seal against the container, and threads to connect to whatever fittings you need. Some have outside threads on only one side, or you can get them with inside and outside threads on both sides, and they cone in all sorts of different sizes and materials.

You can screw in a 6mm push-fit connector, for example: