I would be willing to guess you have a loose headset.

You can tighten bolts, and it won't cure it unless you do it in the right order.

First, loosen the two bolts on the stem along the shaft of the steer tube. They usually are the two bolts closest to the saddle.

When those are loose, tighten the single bolt on top of the stem. It sits in the center of a circular disk. Tighten it snug with two fingers.

The cap that that bolt sits in should be pressing down on the edge of the stem. If it is pressing down on the steer tube inside, it will never get tight and your headset will keep clunking and giving you that noise. Take it to the bike shop to have them give you another spacer or to cut the steer tube shorter.

If the top cap pressed cleanly against the stem, the play and the clunk should be gone.

Tighten the two bolts on the stem along the steer tube. You are done.

It is unlikely that loose handle bars would make a clunking. You likely would notice them shift or rotate out of alignment. Likewise, a loose stem would likely come out of alignment and show itself as the culprit.