Hello and welcome to the forum. I'm also a fairly new Barchetta owner but I'm happy to share my experiences so far.
Firstly, if you're not already familiar with it then track down a link to
ePer which is the system for viewing Fiat parts diagrams and that can help identify the part number you need.
I've assumed that, from your profile, you're UK based, my apologies if that is incorrect.
There are a number of online parts suppliers that offer service parts for the Barchetta. A lot of them seem to be different fronts for
https://www.autodoc.co.uk/ who I've used successfully for a few parts
There is a UK based supplier
https://www.shop4parts.co.uk/ who I've spoken to but not yet ordered from, they stock some B parts and were very helpful when I rang them.
Another one I've heard of but not used is
https://www.ricambio.co.uk/
You'll hear Henk mentioned a lot. He runs
https://barchettaparts.com/en/shop and has a lot of Barchetta specific parts as well as a fund of knowledge about the Barchetta.
The UK Fiat Barchetta owners club
http://fiatbarchetta.uk/ also maintains a list of member recommended garages.
Hopefully others will be along shortly with their suggestions.
Good luck with your B