  For a finite group $G$, we denote by ${\sf d}(G)$ and by ${\sf E}(G)$,
respectively, the small Davenport constant and the Gao constant of $G$. Let
$C_n$ be the cyclic group of order $n$ and let $G_{m,n,s} = C_n \rtimes_s C_m$
be a metacyclic group. In [J. Bass; {\em Improving the Erd\H{o}s-Ginzburg-Ziv
theorem for some non-abelian groups.} J. Number Theory {\bf 126} (2007),
217-236, Conjecture 17], Bass conjectured that ${\sf d}(G_{m,n,s}) = m+n-2$ and
${\sf E}(G_{m,n,s}) = mn+m+n-2$ provided $ord_n(s) = m$. In this paper, we show
that the assumption $ord_n(s) = m$ is essential and cannot be removed.
Moreover, if we suppose that Bass' conjecture holds for $G_{m,n,s}$ and the
$mn$-product-one free sequences of maximal length are well behaved, then Bass
conjecture also holds for $G_{2m,2n,r}$, where $r^2 \equiv s \pmod n$.
