In this work, the infrared active modes are computed for homogeneous bundles of single-walled boron nitride nanotubes (BBNNTs), using the so-called spectral moments method. The dependence of the wavenumber on these modes in terms of diameters, lengths, and numbers of tubes, is investigated. To this end, use is made of a Lennard-Jones potential for describing the van der Waals interactions between tubes in a bundle. We find that, for a finite homogeneous bundle, additional modes appear as a specific signature. Finally, these results are useful for the interpretation of the experimental infrared spectra of BBNNTs.