The exact scattering by a sphere centered on a Bessel beam is expressed as a partial wave series involving the scattering angle relative to the beam axis and the conical angle of the wave vector components of the Bessel beam. The sphere is assumed to have isotropic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The scattered partial waves in the Bessel beam case are also proportional to the same partial-wave coefficient but now the weighting factor depends on the properties of the Bessel beam. When the wavenumber-radius product ka is large, for rigid or soft spheres the scattering is peaked in the backward and forward directions along the beam axis as well as in the direction of the conical angle. These properties are geometrically explained and some symmetry properties are noted. The formulation is also suitable for elastic and fluid spheres. A partial wave expansion of the Bessel beam is noted.