This isn't all that unusual - many bikes will do it at a particular speed, even when all is well.
But yours shouldn't do it at all speeds.
The way I look at it is thus:
It's a miracle the bike doesn't wobble and wiggle it's way off the road even with your hands on the bars...
So, everything has to be just so - and a worn out tire - very square - could easily cause the problem.
A list of what could cause the problem:
the steering head bearings,
swing arm bearings,
wheel bearings,
swing arm side to side positioning,
rim straightness,
wheel balance,
condition of BOTH tires,
fork leg straightness,
fork yokes alignment,
frame alignment (minor crash can tweak the frame easily),
excess weight at the rear,
loose saddlebag mounts,
loose rear subframe mount bolts,
incorrectly adjusted swing arm bearings,
fork oil type, age, and weight,
fork damping components,
rear shock, same things as for fork,
fairing mounting,
large tankbag,
fat passenger,
and I'm sure I've missed a few.
Have a thorough check, and if you're not an experienced mechanic have your dealer check the bearings out - they can be difficult to discern a problem unless you really know what you're doing.
Oh yeah, and change the tire.
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Grant Johnson
Seek, and ye shall find.
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One world, Two wheels.
www.HorizonsUnlimited.com