Bryant nominated Terri Herring of Ridgeland for a six-year term, starting July 1.
State law specifies the 11 board members must come from certain parts of Mississippi.
Two must be from each of the four congressional districts, totaling eight members.
Three must come from state Supreme Court districts — one each from northern, central and southern.
There are already enough board members from the central Mississippi districts where Herring lives. But the board would be one member short from the north.