We demonstrate theoretical stationary and dynamical generation of Bell states in a system of two parallel double quantum dots with one mobile electron each (proposed as two charge qubits) driven by an external potential difference applied to the second of the double dots. For coherent dynamics, it is shown that each one of the four Bell states is obtained through a suitable nonentangled initial condition as well as through the control of the time-dependent external electric field. We analyze dissipative effects on such state formation, due to the coupling with a thermal bath of phonons. Via a Markovian master equation approach, which includes the electron-phonon interaction, we found that Bell-state probabilities are preserved for very low temperature but are adversely affected as the temperature increases. In addition, we include concurrence and charge distribution calculations in order to characterize the double-dot array. This electrostatic mechanism could be of interest in quantum-computation, -information, and -communication schemes.