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We propose a new route to accelerate molecular dynamics through the use of velocity jump processes allowing for an adaptive time-step specific to each atom-atom pair (2-body) interactions. We start by introducing the formalism of the new velocity jump molecular dynamics, ergodic with respect to the canonical measure. We then introduce the new BOUNCE integrator that allows for long-range forces to be evaluated at random and optimal time-steps, leading to strong savings in direct space. The accuracy and computational performances of a first BOUNCE implementation dedicated to classical (non-polarizable) force fields is tested in the cases of pure direct-space droplet-like simulations and of periodic boundary conditions (PBC) simulations using Smooth Particule Mesh Ewald. An analysis of the capability of BOUNCE to reproduce several condensed phase properties is provided. Since electrostatics and van der Waals 2-body contributions are evaluated much less often than with standard integrators using a 1fs timestep, up to a 400 % direct-space acceleration is observed. Applying the reversible reference system propagator algorithms (RESPA(1)) to reciprocal space (many-body) interactions allows BOUNCE-RESPA(1) to maintain large speedups in PBC while maintaining precision. Overall, we show that replacing the BAOAB integrator by the BOUNCE adaptive framework preserves a similar accuracy and leads to significant computational savings.