Here’s a popular one to start www.bikebandit.com Also my local dealer has his parts at a slight discount www.pure-triumph.com People often get stuff from FleaBay too.
They are an actual triumph dealer, not just a parts supplier! As Joe said they know what they are doing and been in business for quite a while with outstanding service.
I recently bought some accessories for my '13 Roadster from 2WheelPros. They had a great deal on them at thew time. They have all parts available as well. 2012 Triumph OEM Road Motorcycle Parts