In the 1H monolayer transition metal dichalcogenide, the inversion symmetry is broken, while the reflection symmetry is maintained. On the other hand, in the bilayer, the inversion symmetry is restored, but the reflection symmetry is broken. As a consequence of these contrasting symmetries, here we show that bilayer WS2 exhibits a quantum confined Stark effect (QCSE) that is linear with the applied out-of-plane electric field, in contrast to a quadratic one for a monolayer. The interplay between the unique layer degree of freedom in the bilayer and the field driven partial interconversion between intralayer and interlayer excitons generates a giant tunability of the exciton oscillator strength. This makes bilayer WS2 a promising candidate for an atomically thin, tunable electro-absorption modulator at the exciton resonance, particularly when stacked on top of a graphene layer that provides an ultrafast nonradiative relaxation channel. By tweaking the biasing configuration, we further show that the excitonic response can be largely tuned through electrostatic doping, by efficiently transferring the oscillator strength from neutral to charged exciton. The findings are prospective toward highly tunable, atomically thin, compact, and light, on chip, reconfigurable components for next generation optoelectronics.