From the "DICTIONARY OF TRANSPORTS AND COMBATANT VESSELS, STEAM AND SAIL, EMPLOYED BY THE UNION ARMY, 1861-1865," compiled by Charles Dana Gibson and E. Kay Gibson, published by Ensign Press, Camden, Maine, 1995, page 217:

MARY BURTON; steamer; tonnage unknown: date of initial service to Army is unknown. The "BURTON" was reported to have passed Baton Rouge heading upriver with troops on May 14, 1862. Reported as having been "turn[ed] over to Army" for $15,000 in late spring of 1862.

References are shown as the ORN, series 1, volume 18, and Record Group 92, Quartermaster Records, at the National Archives.