Experiment discoveries:

Singer 27 “Memphis” has a bobbin that is compatible with this particular Bradbury machine.

Needle in Singer 27 “Memphis” worked but only after I dropped it down a wee bit.

For more information, you can check out these links:
https://sewalot.com/bradbury_sewing_machines.htm, http://www.sewmuse.co.uk/bradbury/bradburyindex2.htm, or http://ismacs.net/bradbury/home.html.