Let $M_{n+1}$ be a fibre bundle with $S_1$ as the base and $n$-dimensional CW complex $F_n$ as the fibre. Assume $M_{n+1}$ is oriented.

(1) Can one show that **$M_{n+1}$ is always a boundary of a CW complex $M_{n+2}$,
where $M_{n+2}$ is a fibre bundle with $S_1$ as the base and $(n+1)$-dimensional CW complex $F_{n+1}$ as the fibre**?

(2) Can one show that **$M_{n+1}$ is always a boundary of a CW complex $N_{n+2}$,
where $N_{n+2}$ is a fibre bundle with a disk $D_2$ as the base and $n$-dimensional CW complex $F_{n}$ as the fibre**?

Edit: Based on the discussions below, one needs to replace the term "CW complex" above by term "manifold" or "topological manifold". This maybe the key issue of my question: when (1) will be valid?

4more comments