We present an adaptive mesoscale model for carbon nanotube (CNT) systems. In our model, CNTs are represented as a chain of nodes connected by tensile and torsion springs to describe stretching and bending of the chain with intermolecular interactions being calculated using a mesoscopic Lennard-Jones potential. Computational adaptivity was achieved by dynamically adjusting node spacing and number during the simulation to optimise the number of simulated particles and lower computational effort. Adaptive simulations were up to five times faster than non-adaptive ones whilst quantitatively preserving all system dynamics. In particular, the model enables the study of the timescale of CNT bundling that leads to the formation of dilute CNT networks, so-called aerogels. These aerogels constitute the first step in the direct spinning of CNT fibres from chemical vapour deposition synthesis. Understanding the factors governing CNT bundling and network formation is key to controlling CNT fibre microstructure, and therefore optimising their properties. Using the model, we simulated the bundling dynamics of two CNTs with an initial point contact at varying angles for CNT lengths of up to 10 µm. We find that bundling times are an increasing function of initial collision angle and follow a power law with increasing CNT length that range from 10−1 to 103 ns. We postulate that when this bundling time becomes of the same order as the CNT bundle collision time, the aerogel will form.