  We show that a Sergeev-Veselov difference operator of rational
Macdonald-Ruijsenaars (MR) type for the deformed root system $BC(l,1)$
preserves a ring of quasi-invariants in the case of non-negative integer values
of the multiplicity parameters. We prove that in this case the operator admits
a (multidimensional) Baker-Akhiezer eigenfunction, which depends on spectral
parameters and which is, moreover, as a function of the spectral variables an
eigenfunction for the (trigonometric) generalised Calogero-Moser-Sutherland
(CMS) Hamiltonian for $BC(l,1)$. By an analytic continuation argument, we
generalise this eigenfunction also to the case of more general complex values
of the multiplicities. This leads to a bispectral duality statement for the
corresponding MR and CMS systems of type $BC(l,1)$.
