Oh yes! Good idea, Frus! You'd be combining your commute AND your aerobic exercise - you'd get a lot more time to yourself and it'd be cheaper in the long run.
I've never heard of anyone getting mugged while they were actually on a bike - you would just need to take sensible precautions like wearing light reflective clothing, carrying a personal alarm and keeping your wallet/purse tucked inside your clothes.
I know its not the same thing but perhaps you could do some kind of time calculation based on your speed on an exercise bike.