Ive seen many warped neck and just curious why most of the warped neck bows on the E string side? despite of the stronger tesion of D and G string..?
Well, neck warpage usually has very little to do with string tension. When a slab of maple making up a bass neck bows or twists, it does it because it wants to. It has internal stress in the different layers of its grain, because the tree was partly bent or twisted as it grew. And/or the board cut from the log may not have been dried out evenly, for long enough. One side of the board may have more moisture content than the other.
When the board is sawn and carved into the shape of a bass neck, whatever internal balance of the internal stresses and moisture content that was there, gets un-balanced. Because a big part of the wood is cut away. So the neck starts slowly bending and twisting, all by itself. It doesn't matter whether the strings are on or off, the wood is bending because it wants to.
Now, if it's trying to bow forward, having the strings on there under tension may exaggerate the bow, because of the springiness of the neck. And when you loosen the strings, the bowing may spring back partway. But that's just the springiness of the neck. The string tension did not
cause the bowing. Taking the strings off will not stop the bowing. If the neck wood wants to bow, it's gonna bow and twist until its personal internal stresses are relieved. It doesn't care about you and your silly string action.
One exception to this is the "Ski Jump" or "12th Fret Kink" condition. That's where the neck develops a slight bend around the 12th fret area, and that is actually caused by the tension load of the strings. The back side of the neck stretches because of the load of the strings. That condition is not warpage from internal stresses or moisture. We talk all about ski jumps and how to fix them up in a long thread in the Pro Bench section, if you are interested:
https://www.talkbass.com/threads/getting-the-facts-about-ski-jumps.1111265/
But normal bows and twisting along the length of the neck are not caused by string tension. The strings may pull the bow a little farther, temporarily, but they didn't cause it.
To your original question: Why is neck bow often greater on the bass side, under the E string?
That has to do with how the growth rings within the board are positioned in the finished neck. When a maple board has internal stresses and decides it wants to bow to relieve them, the direction in which it will start bending is usually predictable. If you look at the end grain of the board, on the heel of the neck, you can see the segments of the rings. They may go nearly straight across horizontally, which is called Flatsawn, or they may go nearly vertical, which is called Quartersawn. Or, more likely, they go at some angle across the heel, somewhere between horizontal and vertical.
The angle of those rings will usually determine which direction the neck will bow or twist, if it decides to relieve its internal stresses. The wood usually tries to bow toward the center of the rings. If you drew the rings out into an imaginary circle, the far end of the board will try to pull in toward the original center of the log.
A neck that is flatsawn, with the ring segments facing curvature-up, will bow straight up. As if the strings had caused it. And the truss rod can work directly to help pull it back. If the neck is flatsawn, with the rings facing down, it will bow down, into a back-bow. A neck that is cut quartersawn should only bow sideways, but they usually mostly twist. A neck that has rings on a partial angle from horizontal will bow upward at some angle, more on one side than the other.
When you see a Fender-style bolt-on neck which has bowed upward, but more on the bass side, look at the rings on the heel. They will usually be flatsawn, curved up, but leaning at somewhat of an angle toward the bass side. I'm not sure why Fender-style necks seem to end up this way more often than not. I think it has to do with how they position their rough sawing pattern on the board, when they are cutting a board up into neck blanks.
There are a lot of techniques that we Luthiers use when building necks to keep the wood from bowing and twisting, and control which direction it moves, if at all. We can make necks that are stable. But these methods are too expensive for most of the manufacturers to do on the production line. So they take their chances on some percentage of their necks warping when they get out into the field.
If you are interested in this whole subject of building fine bass necks, aligning the rings and grain, multilaminate necks, etc., we have a long thread over on Luthier's Corner that goes into much more detail:
https://www.talkbass.com/threads/about-that-quartersawn-maple.1265053/