^^^^^Where did you hear this? Don't take any more advise from whoever told you that.
Losing weight, until you get to a fairly low BF%, is a simple matter of calories in - calories out. According to what you posted above, you're only taking in about 1700 - 2000 cals and your carbs are way too low to be at that much of a calorie deficit. That's not nearly enough energy to sustain your muscle mass, especially without a re-feed day to replenish muscle glycogen. If you lose more than 2 lbs a week, you're being counterproductive as you're losing LBM and BF at the same rate. I'm sure you don't want to be 20lbs lighter at the same BF%.
IMO, the best way to lose BF while sparing muscle mass is to eat at or slightly below your TDEE or maintenance cals while doing 6 - 10 hrs of cardio per week. Your muscle mass needs fuel to sustain itself, so keep calories as high as possible while creating a calorie deficit via intense cardio everyday or even twice a day if possible. 20 min on a bike is essentially worthless and IMO is irrelevant.
Everyone is different, but I like to do 1 hr a.m. med intensity cardio after a protein shake or just BCAA's depending on current BF%. That way you're burning a ton of cals in a somewhat depleted state while having the rest of the day to feed the needs of your LBM.