Your plan sounds feasible.

To start with I would do 10 mile rides, if you can find a flattish ride with not too many cars, hopefully with nice scenery then you will come back, and do it again

I would suggest you ride 3 times a week, your arse will hurt until you get used to it, but once you do, after about 3 weeks, it will be fine- only your lungs and legs will hurt!

Then your lungs will catch up, and you'll feel better. When you reach this stage, after about 3 weeks, mind you, I would suggest trying to increase the distance or intensity of your rides. I would choose distance, myself, the joy of cycling is to be had riding on country lanes in the lovely summer weather.

It might take 2-3 months but you will find a definite improvement in your fitness, general well being and, hopefully, a love for cycling if you keep it up. Some people even become obsessed with cycling (perish the thought)

Good luck, let us know how it goes