Assuming the laser is the “Mecpow X4 PRO 22W” in your profile, it won’t do anything to a metal bracelet without a marking spray, which will be rather expensive for one-at-a-time small items where most of the spray lands around the engraving area.
You must mask off the area outside of the engraving to keep the spray out of the links / buckles / leather / whatever. Removing the spray requires a generous supply of water and rags.
Also, plan on a long extension cord / generator / power pack with enough capacity for a day’s worth of laser action. This discussion covers some of the possibilities:
If all the bracelets are the same, you can use a fixture. If they’re different, then each one requires careful location and alignment. Perhaps you can make a fixture with slots for the most common shapes.
That might be a good reason to set up a personalized bracelet shop, rather than trying to deal with whatever oddball stuff shows up.