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In 1H monolayer transition metal dichalcogenide, the inversion symmetry is broken, while the reflection symmetry is maintained. On the contrary, 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 WS$_2$ exhibits a quantum confined Stark effect (QCSE) that is linear with the applied out-of-plane electric field, in contrary to a quadratic one for a monolayer. The interplay between the unique layer degree of freedom in the bilayer and the field driven partial inter-conversion between intra-layer and inter-layer excitons generates a giant tunability of the exciton oscillator strength. This makes bilayer WS$_2$ 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 ultra-fast non-radiative 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 towards highly tunable, atomically thin, compact and light, on chip, reconfigurable components for next generation optoelectronics.