  The complex structure and magnetism of Pr$_{2-x}$Bi$_x$Ru$_2$O$_7$ was
investigated by neutron scattering and EXAFS. Pr has an approximate doublet
ground-state and the first excited state is a singlet. This overall crystal
field level scheme is similar to metallic Pr$_2$Ir$_2$O$_7$, which is also
reported here. While the B-site (Ru) is well ordered throughout, this is not
the case for the A-site (Pr/Bi). A distribution of the Pr-O2 bond length
indicates the Pr environment is not uniform even for $x=0$. The Bi environment
is highly disordered ostensibly due to the 6s lone pairs on Bi$^{3+}$.
Correspondingly we find the non-Kramers doublet ground state degeneracy
otherwise anticipated for Pr in the pyrochlore structure is lifted so as to
produce a quadrupolar singlet ground state with a spatially varying energy gap.
For $x=0$, below T$_N$, the Ru sublattice orders antiferromagnetically, with
propagation vector \textbf{k}= (0,0,0), as for Y$_2$Ru$_2$O$_7$. No ordering
associated with the Pr sublattice is observed down to 100 mK. The low energy
magnetic response of Pr$_{2-x}$Bi$_x$Ru$_2$O$_7$ features a broad spectrum of
magnetic excitations associated with inhomogeneous splitting of the Pr
quasi-doublet ground state. For $x=0$ ($x=0.97$) the spectrum is temperature
dependent (independent). It appears disorder associated with Bi alloying
enhances the inhomogeneous Pr crystal field level splitting so that inter-site
interactions become irrelevant for $x=0.97$. The structural complexity for the
A-site may be reflected in the hysteretic uniform magnetization of B-site
ruthenium in the N\'{e}el phase.
