She is your child....there's no such thing as offending her, because she is not just your child but your responsibility. If she is doing drugs, then she has lost her sense of responsibility. If she's not doing drugs, then she has nothing to worry about, you'll look like the bad guy as usual, but at least you'll know she's not using drugs. If she is using drugs and you never tested her, and she gets into worse trouble, you'll always wish you had of tested her. Additionally, it's her own behavior that is causing you to want to do this. If she was getting good grades and doing well as you know she can, you might not have suggested it. Either way, she has to take the responsibility for her actions.
I welcome your thoughts, let me know if you want to talk more
On another note, Charlene (another JA expert) suggested that you might be able to have the doctor do the bloodwork and not tell her (daughter) what it was for. This way she wouldn't be offended....if you found out there were no drugs or were drugs, you would know where to go from there.