I see that many busts are attached to bases with brass rods with an attachment to cover the hole in the base. I am at a loss as to where to obtain these.
Any help would be appreciated.

Most model shops tend to stock them, here is a link to a model shop in Canada that stocks it, just scroll down to Metals-Brass and there you will find Brass Rod.

http://actionhobby.ca/catalog/

Steve

You can also try engineering suppliers for brazing rod....

Thanks for the info

While these may not be brass, El Greco sell metal 'bust supports' which appear to do what you require:-
https://www.elgrecominiatures.co.uk/collections/bases-plinths

Cheers,
Andrew

We stock Albion Alloys brass rod and tube, what sort of size are you after.

The Allbion alloysbrass rods and tubes are also great for making armatures.
Bestt wishes, Gary.