J.L.
Next time, get checked for a bacterial skin infection...not bug bite. Skin infections can look like bug bites, and often be misdiagnosed. You ay need an antibiotic. Read up on skin infections...particularly MRSA. It looks like an infected bug bite in the early stages - appears like pimple like bumps.
Another possibility is latex sensitivity. Many bras have latex/spandex in the fabric and that can cause an allergic reaction in some people...reactions that look like bug bites. To remedy the situation, try organic cotton lingere. Yes, it does exist...but it's really expensive. Just google it and you'll find it.
Maybe it's body acne. Just like your face, if you're oily and sweaty there, glands can get blocked and make zits. Use a soap that will get rid of the oily dirt like Neutrogena and see if that helps.
Last but not least, perhaps it's a heat rash or dermatitis. You say it's under the band in the same spot. Perhaps you're not getting enough air circulation there. Try cotton bras and/or use a powder (like Gold Bond) to absorb sweat and see if that helps. Perhaps even cortisone cream or an antifungal might work too.