Consider the "Cotton Carrier". Here's a cheesy promotional video: Cotton Carrier Camera Systems Action Video - YouTube

I have it, and yes, I have used it while biking. I was going to photograph a bike race and I thought it would be rather stupid to drive there - plus parking would be nonexistent. To be honest, I find the Cotton Carrier less than ideal if you're using the camera under "normal" circumstances; like you, I have Black Rapid straps. However, I was concerned about bumps and rattles while on the bike if I put my cameras into my basket or in panniers or strapped to the back rack. I figured if it was strapped to me, my body would provide the best shock absorption. I wasn't too keen on putting all my gear in a backpack because if I fell, I'd likely end up on my back or side, crush all my equipment, and likely hurt me in the process.

So, I split up my kit: camera on me via the Carrier; and accessories in a messenger bag. For you reference, I carried a Nikon D3s with a 70-200 f2.8 - a pretty large and bulky setup. It was a bit awkward, but it worked fairly well overall. The Cotton Carrier is a bit geeky, but for these circumstances, it worked well: my hands were free, and it was centered nicely on my body.

Good luck!