Do you also have the 3' cable with the Motorola logo in the plug? This is very important also.
Using a third-party charger or cable MIGHT NOT cause any problem at all.
Using a third-party charge or cable COULD cause any kind of mayhem.
Many people use third-party chargers and cables and have no problems and will tell you it is a good way to save money. They were the lucky ones.
The approach ...
Get the OEM charger and cable.
Use them and that is your benchmark.
Try other things if you like and you can always return to the Motorola equipment if you run into trouble.
You can damage the battery and/or Bionic with problems from some third-party equipment.
What makes Motorola so good ... they have stringent quality control and the bad units just don't make it out of the factory.