  The non-observation of baryon number violation suggests that the scale of
baryon-number violating interactions at zero temperature is comparable to the
GUT scale. However, the pertinent measurements involve hadrons made of the
first-generation quarks, such as protons and neutrons. One may therefore
entertain the idea that new flavour physics breaks baryon number at a much
lower scale, but only in the coupling to a third generation quark, leading to
observable baryon-number violating $b$-hadron decay rates. In this paper we
show that indirect constraints on the new physics scale $\Lambda_{\rm BNV}$
from the existing bounds on the proton lifetime do not allow for this
possibility. For this purpose we consider the three dominant proton decay
channels $p \to \ell^+ \nu_\ell \bar{\nu}$, $p \to \pi^+ \bar{\nu}$ and $p \to
\pi^0 \ell^+$ mediated by a virtual bottom quark.
