ya, you can actually "burn muscle." In times of caloric need, you can definitely catabolize the proteins in muscle. Like was mentioned before, you will use stored glucose/glycogen and fat mostly first, but eventually, you will start to break down actual muscle protein.
My advice, stop biking, don't eat a ton of protein, and let the muscles do what they will. If you stop biking and start running more, my guess is you will start looking more like a runner without trying that hard. A little extra strength never hurt anybody. Just run, and let your muscles build or atrophy as needed.