Strong light-matter interactions in layered transition metal dichalcogenides (TMDs) open up vivid possibilities for novel exciton-based devices. The optical properties of TMDs are dominated mostly by the tightly bound excitons and more complex quasiparticles, the biexcitons. Instead of physically exfoliated monolayers, the solvent-mediated chemical exfoliation of these 2D crystals is a cost-effective, large-scale production method suitable for real device applications. We explore the ultrafast excitonic processes in WS$_{2}$ dispersion using broadband femtosecond pump-probe spectroscopy at room temperature. We detect the biexcitons experimentally and calculate their binding energies, in excellent agreement with earlier theoretical predictions. Using many-body physics, we show that the excitons act like Weiner-Mott excitons and explain the origin of excitons via first-principles calculations. Our detailed time-resolved investigation provides ultrafast radiative and non-radiative lifetimes of excitons and biexcitons in WS$_{2}$. Indeed, our results demonstrate the potential for excitonic quasiparticle-controlled TMDs-based devices operating at room temperature.