Adsorption onto carbon nanotube bundles may find use in various applications such as gas preconcentration and separation, and as a result, it is of great interest to study the adsorption properties of such bundles. The adsorption of linear alkanes, with their systematic variation through chain length, is particularly useful to explore the effects of molecular length on adsorption characteristics. We have conducted grand-canonical Monte Carlo simulations of light linear alkanes adsorbing onto closed nanotube bundles to explore these effects in a systematic manner. Our results demonstrate how adsorption into the grooves of the bundle is favored with alignment of the alkanes along the nanotube axis. We describe in detail the effects of competition for adsorption in the grooves and on the bundle as a whole, and highlight how selectivity can be tuned through careful choice of pressure and temperature. Finally, we describe how it is possible to derive a systematic relation between the length of the alkane and its loading on the bundle, and discuss its usefulness in applying ideal adsorbed solution theory (LAST) to predicting competitive mixed adsorption over a wide range of pressures. We also focus in turn on the ability of LAST to capture adsorption-saturation effects.