How long does it take for a bone graft to grow?

It doesn't grow: Bone graft does not "grow" it serves as a scaffold for your own bone. Your bdy removes the bone graft and replaces it with your own live bone. Depending on the size of the graft it can take several months unto a year , year and a half.

4 weeks to 4 months: Bone graft material will act as a catalyst to begin bone growth via osteoconduction, osteoinduction, or osteogenesis. In osteoconduction, the grat acts as a scaffold, as blood vessel via neovascular genesis will bring in the bone cell, proliferate, differentiate, and mature. In osteoinduction, it will induce the bone to form and mature similarly. Osteogenesis only occurs with autogenous graft.