The most obvious to check is the tyres. First check tyrepressure; about 2-2,2 front and a little more back. Second is the type of tyres. Always try to have as close to original equipment as possible. As I know Bridgestone BT45 does wonders for the TR1.! Tyres that are too wide or have weak sidewalls soon destroys the mild manners of the bike.
The bearings can bee worn, most often in the rear wheel due to a too tight chain. Check - adjust - renew wheel bearings and steering ditto.
Good Luck!