I agree with Bill; the distance between the tailpiece and bridge does not affect string tension.
The tailpiece does need to be far enough away from the bridge so that the string, after passing over the saddle, does not hit the back rail of the bridge.
As Bill pointed out, the angle of bend in the string over the saddle needs to be sufficient enough to keep the energy of the string from passing over the saddle.
The saddle of the highest pitched string, which on a standard tuned four string bass would be the G string, is the furthest away from the back rail of the bridge, and thus might be the most important in determining the best distance for the tailpiece.
As you suggest, some tailpiece placements are chosen because the owner wants to use a particular set of strings on the instrument and needs to accommodate thread wraps and/or exposed cores.