First, I would say that any physical activity you add to your daily routine is "good exercise."
Second, I agree that bike riding works the legs, but not the muscles in your arms and upper body. However, you are forgetting some vitally important body parts – the heart and lungs.
Bike riding falls into the category of aerobic training. To get the most health benefit from aerobic exercise you should try to maintain a level of moderate intensity for at least 30 minutes most days of the week. (An hour a day would be terrific.)
Your heart rate should be at 60% to 75% of your maximal heart rate. The simple way to calculate this is to subtract your age from 220. For example, if you're 50, your maximal heart rate is 220 – 50, or 170. Sixty percent of that is 102; 75 percent is 128. So a 50-year-old would aim for heart rate between 102 and 128.
But don't rely on this measurement alone. At moderate intensity exercise, you should be able to talk without difficulty, even if your heart rate is in range. If you are breathing so hard that you can't talk, you may want to ease up a little.
To make up for the muscle exercise that bike riding lacks, I recommend adding resistance training with weights or machines to work your arm, shoulder and back muscles. Do this 2 to 3 times per week. Don't do resistance training of the same muscles two days in a row. They need a chance to recover.
I also suggest adding core strengthening to work your abdominal muscles. Although you don't need to, you can do sit-ups and crunches daily.