Both players sustained injury in last week’s defeat at Rotherham, with Beestin set to be out for between six and eight weeks after damaging ankle ligaments.
On-loan defender Anderson has returned to parent club Burnley and will have surgery to repair a fractured cheekbone. He will be sidelined for up to six weeks.
Joe Wright is hoping to return to contention after recovering from fractured ribs, but fellow centre-half Andy Butler (knee) is still unavailable.
Bury could be boosted by the return to contention of versatile defender Craig Jones.
Jones has returned to training after recovering from a thigh injury, which has kept him out since early January.
Fellow defender Nathan Cameron is expected to be fit to resume as he continues to manage a troublesome knee.
Striker Jermaine Beckford and defender Eoghan O’Connell (both knee) remain sidelined as the Shakers bid for back-to-back league wins for the first time this season.
Cardiff remain unhappy with Derby's decision to postpone Sunday's Sky Bet Championship game at Pride Park.
Dundee United boss Csaba Laszlo has been left hoping for St Mirren to slip up in the race to seal promotion to the Ladbrokes Premiership.
Crewe will consider starting Chris Dagnall when they host Forest Green on Tuesday.