Flhtr
Is your Triumph a blued barrel or a Weather Shield?
When you say rust - I guess I would ask is a rust spot or when you wipe the barrel you are seeing signs of rust on you wiping rag?
If it is a blued barrel, and you are wiping a bit of rust - that kinda is normal with a new gun... The blueing process is a rusting process. If this is the case I would suggest you wipe the barrel action clean with some alcohol - let it dry completely and then wipe a high quality oil on the barrel, wipe it on liberally so it almost has standing oil on the metal. The oil will eventually neutralize the blueing process but it will take a couple occasions of wiping oil on to get the blueing neutralized.