It works by burning calories. Unfortunately in practice it's not easy to figure out. Some things to consider:

Strength training is an important part of overall health, but you're burning more calories doing cardio than when you're lifting weights.

What is the total cardio time for the different workouts? And how do they compare in intensity? If the bike ride days have more cardio time at the same intensity as the drive days, then the bike ride days burn more calories. If the bike ride days are easier workouts over a longer time, you might actually burn fewer calories on those days.

If you have more energy when you drive, it might be because you're not fueling (eating) enough on the days you're riding your bike. A pre-ride workout meal or snack can help you work harder.

If you want to lose weight and keep it off, it's best to do it in a way that does not exhaust you and make you miserable and therefore make you burn out. Also you need to vary the intensity of workouts to give yourself easy days (or days off) so your body can recover from the hard workouts.

Also, read this book:

http://www.nancyclarkrd.com/books/sportsnutrition.asp

Good luck!