Richard Bridges married Melvia A. Elliott in March 1866, in Yazoo, so he was back in Yazoo then. He remained in Yazoo until his death in May 1919. I do not know if deserters often returned to their homes and continued to live among those who served throughout the war. Maybe.
You asked about brothers. The 1850 Yazoo County MS US census lists Henry (age 11) Bridges living in the home of John W. Purvis. Perhaps there is a family relationship between these 2 Bridges. I believe this Henry Bridges is H.N. Bridges who served with the 1st MS Lt Artlry Regmt, Co B.
The only family history I gleaned from interviewing Richard Bridges' grandchildren is that he served during the siege of Vicksburg as a courier, swimming the river at night. Apparently he failed to swim out before the surrender in July.