  We define Aeppli and Bott-Chern cohomology for bi-generalized complex
manifolds and show that they are finite dimensional for compact bi-generalized
Hermitian manifolds. For totally bounded double complexes $(A, d', d'')$, we
show that the validity of $d'd''$-lemma is equivalent to having the same
dimension of several cohomology groups. Some calculations of Bott-Chern
cohomology groups of some bi-generalized Hermitian manifolds are given.
