79er,
Place the bike on center stand with the front wheel off the ground.
Slowly turn the handlebars full lock, left to right, back n' forth. Do you feel any
notchiness -if that's a word?- in the steering? Any gritty feeling
could indicate worn out steering head bearings that may have become brinneled.
As Barry noted, if the bars are falling off center with some force, the head bearings could be too loose due to wear or maladjustment by a PO. An inspection, fresh grease and an adjustment may help.
Is the front wheel balanced? Tire pressure correct? Fork fluid levels per spec?
And a final thought... Is the rear swingarm properly torqued? That may be a reach

Monte