It also depends how long you are going to 'spin' for. For example if you were going to work out for 20 mins, I would, as S_M suggested, work off your heartrate, but work as if you were going up and down hills. 4 mins @ 90 RPM/min, 30 seconds @ 120 RPM/min for example. As long as you can feel your heart pumping faster than normal you're doing it right!
Edit to add: Time scale, probably at least 20 mins to be a good work out (excl w/u and cool down) =]
Obviously it all depends how much excersize you do other than 'spinning'...
cycling involves a deeper stroke rate, or deep breathing intake than when your running, i.e. when your run you take shorter sharper breaths more often, whereas with cycling stroke rate is much deeper increasing lung capacity and cardio vascular efficiency, also as you operate at a lower avg bpm whilst cycling, meaning you can go for longer, making it a very effective way of burning calories and placing yourself in an energy deficit ideal for lowering body fat percentage. However it is not a replacement for running but in my experience combining the two can give you very good results, in a 6 week programme combining long bike rides, some long runs and some running speedwork I manged to drop my body fat percentage by around 4-5 percent IIRC, as well as imporving my cv fitness considerably. As a guide aim to cycle at least twice the distance that you would have run, in the sessions you are replacing. If you have access to an ergo rowing machine, high intensity intervals mixed into this would be highly beneficial, the same goes for swimming..... keep your body guessing and don't settle on a set programme for more than about 8 weeks, this will keep you cv system on it's toes and stop you getting bored too!