Have a think about Callanetics for beginners. The video/DVD shows how the routine can be adjusted around physical infirmity. I am severely disabled and bedridden through illness, and I can actually do all the exercises in bed (adapted to suit my limitations). You start at a level suitable to your abilities. The movements are tiny. There's one you can do sitting at a desk, and most you could do watching the TV etc.. They are not high energy or tiring, or I couldn't do them.

Also, the vigorous exercise needn't be done on an exercise bike.. It's basically anything vigorous. 2 minutes of activity is very little. I have just done it in bed, while watching CSI by tapping a pillow for 30 sec. twice, rest, writhing for 30sec. rest, then moving my legs for 30sec. That was pushing my muscles to their limit and I won't manage to do it every day, but my life is very sedentary, and I'd love to use this great technique to improve my health. If I can manage it, almost anyone can.