Reversible transitions between the A- and B-forms of DNA are obtained in free molecular dynamics simulations of a single double helix immersed in a water drop with Na+ counterions. The dynamics of the transitions agrees with their supposed cooperative character. In silico, titration of the transitions was carried out by smooth variation of the drop size. The estimated range of hydration numbers corresponding to the transition roughly agrees with experimental data. The chain length dependence was studied for double helices from 6 to 16 base pairs. It appeared that the B --> A transition is hindered for DNA shorter than one helical turn. With increased NaCl concentration in the drop, stabilization of the B-form is observed accompanied by the salt crystallization. The results strongly suggest that the B --> A transition at low hydration is caused by Na+ ions sandwiched between phosphate strands in the major groove and is driven by direct medium range electrostatic interactions. The role of the reduced water shell apparently consists of increasing the counterion concentration in the opening of the major groove. Analysis of the available experimental data suggests that this mechanism is perhaps generally responsible for the A/B polymorphism in DNA.