Also, check for a fuel leak if it 'smells like gas'. If it is truly running rich I would think it would soon set an FI code.
The only other thing I can think of is a bad O2 sensor.
The O2 sensors (actually they are O2 switches) operate in a narrow band between 14.1 and 15.1 AFR. As they age their effective bandwidth narrows to the point where the system can have difficulty going into closed loop mode.
The bike operates in open loop at many points such as rapid acceleration, wide open throttle and closed throttle deceleration. When the sensor's range drops below where the computer can sense a stable reading it goes into an open loop mode at all points in the map. This default open loop setting is typically quite rich, usually in the 12.7 - 13.1 range.
So, with an 8 year old bike it's highly likely one or more of the sensors have gone out of range and need to be replaced. The dealer's computer should be able to run a test and identify the faulty sensor/s.
BTW, this typically will not throw a code since open loop operation is part of "normal" operation, especially in an '01 bike. Newer bikes, especially from 2010 on will probably throw codes when it can't go closed loop at idle since this is now part of the EPA certification criteria.