Rice is okay, as it's got Amino Acids and Carbs, but it's high GI, so don't go mental with it. Best times would be a moderate portion first thing when bloodsugar is low and after workouts, when it's lowered.
When you need Carbs, go lower GI like Broccoli, Mushrooms, Tomato, Peppers, Beans, Cashews etc, but remember that Mushrooms and Legumes like Beans, have Protein and Carbs, so factor that in to your Carb and / or Protein intake, when adding such foods to meal choices.
As for exercise, don't do the bike ride.
Stick to the morning Cardio and have something first; no Cardio on empty, it's V bad in my opinion and may burn muscle and as a lb of muscle burns an extra 45-50 calories, burning it won't help you lose fat weight, but may eventually help put a bit back on. So fuel first then exercise.
I'd also consider limiting the duration of morining Cardio. Go for something non-adaptive like Intervals and max them at 45 minutes. You might also be advised to have at least 1 day off, preferably 2 for rest and recouperation.
Soif you go for 2 then I'd go 3 days on, 1 off, 2 days on, 1 off, so the off days aren't back to back which could eat into progress if they were and you never go more than 3 days straight of intervals in a week.
Sound okay ?