I so sympathise. I was a J cup when I started power-walking and jogging six months ago, and The Bounce was definitely one of the things that made exercising much more difficult, even unpleasant. I didn't have much faith in sports bras generally, not least because I've always needed under-wired bras. One that really works for me, though, is the "Glamorise Sport No-Bounce Camisole Bra" (paste it into Google, spelt with an S). It's surprisingly supportive and comfortable, not overpriced, and it washes well. It does up at the back and has relatively wide adjustable straps. I'd recommend getting a snug and even tight fit, to hold everything in place more effectively. I wear mine for running every day, for Pilates and at the gym, and it reduces the bounce to barely perceptible levels. Fantastic! I'm now into a DD cup, and have continued to wear the same brand. Hope this helps, but message me if you have any trouble finding one. And well done for getting into interval training!
"There's no secret. You train a lot and eat right" (Mo Farah, British Olympic marathon runner).