I have read somewhere (don't remember where, long time ago) that tea enthusiasts clean their tea pots only with water and without soap. Additionally they only rinse it and don't use a scrub to remove the residues.  Is this actually a good practice or simply a quirk? Consider that I don't always drink the same tea, does this matter? I sometimes add fresh lemon or ginger to the water, I suppose this might be a reason to thoroughly clean the pot, to prevent spoiling?  If it matters: my pot is made of glass. 
How, and if, you clean your tea pot depends both on what your tea pot is made out of, and your personal preference.  The only time I've ever seen it recommended that you avoid cleaning agents entirely when cleaning a tea pot is if it is made out of clay. The reason for using only water is because unfinished clay pots, like Yixing / zisha pots, have very porous walls and will absorb both chemicals and the taste/smell of your soap or other cleaning agent. (For these types of pots, it's also generally recommended to brew only one type of tea per pot, for the same reasons.)  For tea pots made out of other materials, it really comes down to a matter of preference. In many cases (like with glass and ceramic), simply rinsing the pot in hot water immediately after use will suffice most of the time. If you let your brewed tea sit for a very long time in the teapot, or if you are using hard water, you might start to see mineral buildup or brown stains (from the tannins in the tea). These aren't harmful, but many people don't like the way it looks. If you're looking to clean the stains / buildup off your tea pot, do not use bleach - I'd avoid using bleach on any kitchenware, but especially something glass or ceramic that has pores that could absorb the bleach. A simple baking soda solution will work (you probably won't even have to scrub at all for the stains to come out - just soak for a few hours). You could follow the baking soda soak with a run through the dishwasher (if your pot is dishwasher safe) or a quick wash with soap and water if you'd like.  Personally, the only time I wash my (glazed ceramic) teapot is if I brew an Indian chai, which has sugar in it. Then I'll wash it with soap and water because I don't want any remnants of sugar sitting in the bottom of my pot, happily feeding bacteria. But for brewing any black, green, or oolong tea and tisanes without any additions, I just rinse before and after brewing with hot water. As long as you don't see any mold growing in your tea pot and you regularly rinse it with hot/boiling water, you'll probably be fine.  I'm not sure where the anti-soap attitude comes from among modern-day tea drinkers. It could be left over from the days before dish soap existed, it would be an overly obsessive concern with any cleaning agent "ruining" the tea's flavor, or it could just be that they're a little lazy, like me. :) (Tea pots are kind of a pain to clean!)  So, to sum up the answer to your question: with a glass pot, it's totally up to you. I'd wash it with soap and water if you've put anything other than tea leaves and water in the pot, but otherwise, a quick rinse with hot or boiling water should be fine. 