You can't be bonking after one mile unless you have been starving yourself. Bonking is when you run out of glycogen and your muscles can only burn fat for energy. You likely have at least a couple hours of glycogen at moderate exertion levels.
If you are out of shape, you may not have the muscle tone and/or the aerobic capacity to cycle more than a mile or two yet. Assuming that you do not have a medical condition like a heart problem (unlikely, though not unheard of at age 31) you should take it slow at first and not overdo it. You fitness should quickly improve. If it doesn't, then you may need to talk to you doctor about it.
General disclaimer: If you are starting an exercise program, you should consult with your doctor first to ensure your program is safe for you.
Good decision to improve your diet and get exercise. If you stick with it, you'll find it improves almost every aspect of your life.