I suspect that the "Worth Bagley Unit' is not a military unit, but the local camp or post of the United Spanish War Veterans(USWV) organization.
Worth Bagley was the only naval officer kileld during the Spanish American War. There was no "Worth Bagley Unit." His biography is on-line at http://spanamwar.com/bagley.htmhttp://spanamwar.com/bagley.htm
United Spanish War Veterans camps existed in almost every city, and were named for, generally, local heroes. The USWV was open to veterans of the Spanish American War, Philippine American War, and Boxer Rebellion...your relative could have served in any of these.
Your best bet to learn more about him would be to track down his pension records.