“Can a dental bridge cause tooth damage?”

No.

A dental bridge is one of the several treatment options for missing a tooth. Under normal circumstance, a dental bridge will not cause damage to the adjacent teeth. However, if the adjacent teeth are not healthy, or having some other underlying compromise condition, such as periodontal ( gum ) disease, then it will compromise the long term success of a dental bridge.

To create a bridge you need to prepare the neighboring teeth for crowns (which will be attached to the false crown in the middle). When you prepare a tooth for a crown you remove all of the enamel, about the thickness of a nickel from all surfaces. If the tooth next to your missing tooth is healthy then you are taking away a lot of natural tooth structure that could be prevented if an implant is possible. Sometimes teeth can be traumatized by the reduction done for a crown, so yes teeth can be damaged by preparing for a bridge. Another form of damage that can occur is if the neighboring teeth have periodontal disease and are no longer strong enough to support the added stresses of a bridge.

Yes, a dental bridge involves cutting two teeth adjacent to the missing
teeth. Implants are generally preferable given that they are much easier to
clean and they don't require cutting other teeth.