It might be fine if you worked up to that kind of training volume, but be careful of overtraining. Tabatas and other HIIT is supposed to be hard.
I happened to stumble across this post from Robb Wolf just a short while before I saw your question. It's relevant.
Training volume is one of those “U-shaped curves”.... Too little isn’t good and neither is too much. Like Goldilocks’ porridge it has to be “just right”. But it must also be said that having too little is far preferable to having too much. If you’re patient, adding volume in small doses is easy. Fixing an overtraining issue that has built up over a few months isn’t. Recovering from an injury can be even worse.
If you take something designed to last 4 minutes and stretch it to 16 minutes you have drastically changed the training effect.... Tabatas are plenty hard even when done correctly. Try the Dan John special of front squatting 95 pounds for eight rounds. You’ll be cooked. I guarantee it.
Personally, if I did it once a day for a week and I felt fine, I'd feel okay with doing two-a-days. But I sure wouldn't dive into two or three a day without ramping up slowly.
Also, because strength training is so productive in a variety of ways, you might consider supplementing your exercise-bike Tabatas with strength training.