We use liquid phase exfoliation to produce dispersions of molybdenum disulfide (MoS2) nanoflakes in aqueous surfactant solutions. The chemical structures of the bile salt surfactants play a crucial role in the exfoliation and stabilization of MoS2. The resultant MoS2 dispersions are heavily enriched in single and few (<6) layer flakes with large edge to surface area ratio. We use the dispersions to fabricate free-standing polymer composite wide-band saturable absorbers to develop mode-locked and Q-switched fiber lasers, tunable from 1535 to 1565 and 1030 to 1070nm, respectively. We attribute this sub-bandgap optical absorption and its nonlinear saturation behavior to edge-mediated states introduced within the material band-gap of the exfoliated MoS2 nanoflakes.