Main Motorcycle: 2009 Bonneville SE
Join Date: Jun 2009
Location: Asturias, Spain
Other Motorcycle: Yamaha XV1100
Extra Motorcycle: Qingqi QM200GY-BA
The spitting and backfiring through the carbs usually indicates a weak mixture.
Check for the presence and state of the rubber manifold vacuum spigot caps, the carb rubber adaptor tubes and manifold to head joint, although that one doesn't usually give trouble unless it has been disturbed.
Usual procedure: Check vacuum caps visually for cracks and splits, spray something combustible like cleaning alcohol, WD-40, etc around the rubber adaptor joints while the engine is idling.
Listen out for any change in speed or exhaust note as the combustible fluid is sucked in by the vacuum leak.
If the adaptors are the original 2001 parts they could be due for replacement. Check them visually for cracks and splits.
See if tightening the clamps improves things, but there's a limit as to how much more those clamps will go. The rubber tends to collapse with time and the clamps might need to be supplemented with strips of rubber, like strips of old tyre inner tube, etc.