My handlebars shudder when I ride
What should I check for this problem?
At low speeds, this is normal, but at high speeds, not so much. Here are some things to check:
What if the steering head bearings are bad?
If the bearings are too loose, you get a wobble. If too tight, then when going around a long curve, the bike wants to turn, then straighten and repeat rather than taking a smooth arc. If there's no wobble, then tightening the bearings probably won't make much difference; people have ridden with marginal bearings for quite a while.
To adjust them and look for worn bearings, put the bike on the centerstand, and put something under the engine to get the front wheel off the ground. First, try to move the fork legs forward and back, if there is any movement at all, the steering head bearings are loose.
To tighten them, loosen the top nut that is between the fork legs behind/below the ignition. Under that and under the top clamp is another nut with a slotted head. Use a spanner wrench (or a hammer and punch) to tighten this lower nut one tooth at a time. Tighten the top nut before checking the forks again. Loosen the locknut, then tighten the bearings until you can feel a noticeable tightening, then back off a bit, tighten things back up, and go for a test ride. For detailed directions on this procedure, see Steering head bearing replacement.
Once the forward and back movement of the forks is fixed, then you should check for flat spots and over torqueing. Move the handlebars left and right. There should be no difference in the pressure it takes to move them as you go from left to right. Worn bearings will often have a spot right in the middle that the bars want to stay in. Overtightened bearings will not move smoothly.
If you can't find something in between the loose and tight adjustments that feels right, then you need new bearings. Bearings shouldn't go bad for a long time, even with heavy loads put on the bike.