Hello,
For your convenience, I wanted to let you know that this Bunn model is Model TDO-N-4
Here’s a link to the manual: http://download.partstown.com/is-bin/intershop.static/WFS/Reedy-PartsTown-Site/-/en_US/manuals/BU-TDS3S-5S-ICD3S_spm.pdf
And here’s a link to all available parts for this model: http://www.partstown.com/bunn/tdo-n-4/parts/1/0/50#model-tab-content=parts
Finally, on the last page of the manual (that first link), I found this parts list for the faucet:
I believe the threaded plastic piece you are referring to is this: Bunn 03093.0002 WING NUT, FAUCET (BLACK) | Parts Town
I can’t be certain since I don’t have the assembly in front of me, but I believe this list should provide you with what you need.
Have a great day!
John