Sounds like a good approach - another one is is 1 minute walk, 1 minute run. It makes one hell of a difference (the walk should be fairly brisk.) After a couple of weeks, 2 minutes run, 1 minute walk and so on until you're running constantly after several weeks. You can draw out the time you're running too. Start, say with a 20 minute session, then up it by 3-5 minutes every other time. It's a better way to get into it rather than trying to run it constantly each time.
Being a cyclist will help in terms of your base fitness but as you're finding out, different muscles come into play when you're hoofing it.