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Processing boron nitride nanotubes (BNNTs) for applications ranging from nanomedicine to electronics generally requires dispersions of nanotubes that are stable in various compounds and solvents. We show that alcohol/water cosolvents, particularly isopropyl alcohol (IPA), are essential for the complexation of BNNTs with DNA under mild bath sonication. The resulting DNA-wrapped BNNT complexes are highly stable during purification and solvent exchange from cosolvents to water, providing potential for the versatile liquid-phase processing of BNNTs. Via molecular dynamics simulations, we demonstrate that IPA assists in the solvation of BNNTs due to its pseudosurfactant nature by verifying that water is replaced in the solvation layer as IPA is added. We quantify the solvation free energy of BNNTs in various IPA/water mixtures and observe a nonmonotonic trend, highlighting the importance of utilizing solvent-nanotube interactions in nanomaterial dispersions. Additionally, we show that nanotube lengths can be characterized by rheology measurements via determining the viscosity of dilute dispersions of DNA-BNNTs. This represents the bulk sample property in the liquid state, as compared to conventional imaging techniques that require surface deposition and drying. Our results also demonstrate that BNNT dispersions exhibit the rheological behavior of dilute Brownian rigid rods, which can be further exploited for the controlled processing and property enhancement of BNNT-enabled assemblies such as films and fibers.