Walking meditation : http://www.meditationoasis.com/how-to-meditate/simple-meditations/walking-meditation/ is considered as "just as profound as sitting meditation". If we were to extrapolate this idea into a situation where instead of walking you were on a bike, would an expert's opinion consider this meditating on the bike at the gym an effective practice of meditation?
Short Answer: Yes.
The Satipatthana Sutra implies this. Here's a snippet...
Moreover, when a practitioner walks, he is aware, ‘I am walking.’ When he is standing, he is aware, ‘I am standing.’ When he is sitting, he is aware, ‘I am sitting.’ When he is lying down, he is aware, ‘I am lying down.’ In whatever position his body happens to be, he is aware of the position of his body.
Moreover, when the practitioner is going forward or backward, he applies full awareness to his going forward or backward. When he looks in front or looks behind, bends down or stands up, he also applies full awareness to what he is doing. He applies full awareness to wearing the sanghati robe or carrying the alms bowl. When he eats or drinks, chews, or savors the food, he applies full awareness to all this. When passing excrement or urinating, he applies full awareness to this. When he walks, stands, lies down, sits, sleeps or wakes up, speaks or is silent, he shines his awareness on all this.
The gist of the above is that mindfulness should be applied throughout the day -- including time on the exercise bike.
However, I don't think this should replace formal meditation practice. Setting aside time for meditation allows you to better control distractions, which in turn can allow you to go deeper. Meditating on the exercise bike should be done in addition to your regular meditative practice, and should be part of an attempt to maintain continuous mindfulness.
This philosophy (which is used in the 'meditationoasis.com' practice, which you you were asking about), is different from Buddhist philosophy. So the effectiveness cannot compare.
I've always considered the ultimate mindfulness practice to be that which is constant: that is, a meditative state of mind every moment of every day, no matter what else is happening. However if you start by running a marathon before you've trained on smaller runs, your body won't be prepared to fully benefit from the marathon. Similarly, while I think meditating on an exercise bike could be effective, starting with "easier" methods, especially sitting meditation, and careful walking meditation, will build your ability to be successful in other methods.
TL;DR: Better to start small and simple, and eventually, your meditative state of mind will carry over into everything else you do, including exercising.
I am a novice meditator with a stationary bike at home. I find it an easy way to integrate a 20 minute meditation session into a workout. It can be difficult to find the time otherwise. I find it much easier than sitting only as there is a built in focus on your cadence and rhythm and the sensations of a fan and sweat on the skin. If your goal is to be some super athlete no you won't get the best workout. If your goal is to get an hour of moderate exercise while working in some mindfulness zzIt works well. If at a gym you can put on head phones and play white noise or any music or audio you feel helps. I'm not the Dalai Lama but I have found this a method that has actually got me doing it instead of thinking and reading about it for years.