Thanks to All!
I unscrewed the screwer an saw whats up in its innards.
Pigrew, your spec sounds just right, the charger circuit is internal and feeding it 7V DC at 250mA should be the ticket.
It's my guess that the 7V DC is unregulated, the base unit is supplied by a wallwart, but the voltage output to the handle should be around 7V DC more or less at .25A load and I doubt that Bosch would go to the trouble and cost of regulating this voltage into the handle because the handle has a charger chip of some type to carefully charge the LI-Ion cell.
I will construct a LM317 circuit that will be current regulated to offer the handle a cur limit of .25A at 7V and see which way the smoke blows!
Andy3055, I thank you for your input, but I don't think your guess is correct for the charger base voltage, since the internal regulator chip in the driver would need some voltage overhead to function at all. My educated guess is the regulator inside the handle would charge the 2000mAH battery to full charge at a cutoff voltage around 4.0 to 4.2V and at a constant current of around .25A, so 3.6V into the handle would therefor not work without exotic boosting circuitry.