RE: Fluid Transition Routine
Dont think about bulking and cutting.
I'm guessing you are relatively new to training with weights (properly anyway) therefore i would recomend the following.
3 days resistance training (the split, if you choose to do one, is up to you but when you have decided post it up and let me have a look. Only use compound exercises)
3 days cardio. I like the bag but personally i would drop the bike and do walk/ jog intervals if posible. This will lead to greater cal expenditure
Follow a clean diet, there is no need to go on a mega strict cutting diet, at your current size simply eating clean will have the desired effect. 5 or 6 small meals spaced out 3 hours apart each day will be fine. Aprox 1g protein perlb body weight, moderate carbs (no simple stuff) and low fat (essential fats only plus what is present in your protein and carb food)
The good new is that as you are fairly new to training your body will add muscle as you diet as a simple adaptaion to the work you are doing. You are right that this will help your body fat come down but at your current BF level you can add muscle without following a bulking diet.
If your body needs to draw on energy to add extra muscle where do you think it will get it from other than excess food?
The answer is your own bodyfat stores!
Hope that makes sense