What is the most physically painless way to bleach sensitive teeth?

Swish with a little hydroge peroxide and water every say for a couple of weeks. Then brush with Synsodyne

Are you already brushing your teeth with whitening toothpaste?

Have you asked your dentist?
I had dental molds made a few years ago and get a 30% bleaching gel from my dentist. I experience a little sensitivity but nothing unbearable. I usually do a treatment right after my cleanings, and then again, maybe 2–3 weeks later and my teeth stay a very nice white, but also natural looking, not neon.

Same response as @Coloma; I used the dental molds and the dental strength solution.

I just rub mine with a piece of damp gauze dipped in baking soda.

Use sensodyne when bleaching. Lay off bleaching for a few days, then go back to it.