I had one a few days ago (Wednesday) actually!
I had to remove my bra, but I removed my bra with my top still on and had a small towel to protect my modesty, and the doctor slipped her hands under my top to apply the metal thingies. So bra was off, but I wasn't 'exposed'.
The whole experience was a bit bizarre - I'm in Tokyo and their health checks are really rigorous compared to the UK. I had an ECG, Blood tests, urinalysis and a chest X ray, among all the normal stuff (blood pressure etc). Apparently got sinus arrhythmia and bradycardia but won't know anything more about it until I get full results back in two weeks.