The theory of linear magnetic response for the case of uniaxially anisotropic superparamagnetic nanoparticles suspended in a fluid is developed for the situations where, along with the probing field, a stationary bias field is present. The built up description allows for both mechanisms of magnetic relaxation available to the particles: internal (relaxation of the magnetic moment inside the particle) and external (relaxation together with the particle body due to its Brownian orientational diffusion in a fluid). In this framework, the dynamic magnetic susceptibility of a nanosuspension (magnetic fluid) is considered in the high-dilution limit, i.e., neglecting the interparticle interactions. It is proven that the absorption spectrum (the frequency dependence of the out-of-phase component of dynamic susceptibility) in a general case has at least two well-distinctive maxima. The bias field affects thepositions and heights of both these maxima but leave them well resolved. Moreover, in the presence of bias under certain conditions the spectrum acquires a third maximum. The developed theory is used for interpretation of the magnetodynamic measurements on a nanosuspension of cobalt ferrite. A minimally sufficient account for polydispersity of the real sample–three fractions–is shown to provide a fairly good description of the measured spectrum in a wide frequency range.