Most drinking water regulations state that potable water should contain no more than 2mg / Lt copper.
If you drink 2 Lt of water a day then that's a total of 4 mg.
Many tooth pastes contains tin salts and fluoride (which is why you should not swallow it).
Unless your drinking water is really poor quality you probably won't exceed any toxic levels of copper. If you use the brush as directed.
Why are you worried about bacteria on your tooth brush? I would recommend leaving it in alcohol based mouth wash after use, this would kill most bacteria and won't leave your brush tasting metallic.