Can't your cardiologist recommend something? You might be surprised if you asked.
Personally I am afraid to suggest anything since the doc told you to cut the bike and I don't know exactly why you should cut it or why it would be okay to, for example, jog instead of bike, or anything else that gives a comparable cardio workout.
You know what you can and cant do. Here are are a few you can do at home: Burpees
Plyometric push ups
Intensity and reps at your discretion