Striker Becchio missed Saturday's 2-0 defeat at Hull due to a thigh strain, meaning Davide Somma made his first start for the club in 19 months following a serious knee injury.
White received his fifth booking of the season at the KC Stadium and sits out an automatic one-game ban.
Forward Ross McCormack also returned to the starting line-up at Hull and manager Neil Warnock must decide which combination to utilise against Bolton.
Warnock made five changes against the Tigers, opting to start with three central defenders, while White and Sam Byram operated as wing-backs.
Striker El-Hadji Diouf and on-loan winger Jerome Thomas were not included in the squad on Saturday and will be hoping to feature.
Leeds have slipped to successive league defeats at Nottingham Forest and Hull and are now five points adrift of the play-off places in ninth.