Putting it simply: Aerobic means you're using a source of energy that needs external oxygen (fatty acids.) Anaerobic means the intensity of what you're doing exceeds the oxygen your lungs, blood and heart can take in. Your body needs to turn to a source of energy that doesn't require external oxygen to complement the fat burning (Glycogen.) Your glycogen reserves are pretty slim, roughly 600 grams and your body won't let you go below 125 grams (this is when you hit the wall.) Your fat reserves on the other are cheap and cheerful, even for a a very lean person, you got pounds of it. So if you maintain an intensity that allows you to burn mostly fatty acids and maintain your glycogen reserves, you can sustain that exercise for a really long time.
Rule of thumb, ride at the highest pace you can without needing to breath with your mouth open. If you need to open your mouth to breath in, slow down a bit. As the weeks go by, you will find that your ability to burn fat will increase, your pace will go higher and you won't even be out of breath.
That being said, depleting your glycogen reserves once a week will do wonders for your metabolism, insulin sensitivity and your body will reward you for decades to come.