There may be at least four sets of variables to consider here. The first and probably least changeable relate to the design and quality of materials used to construct your bass. The second relate to the set-up such as bridge and string heights, sound post position, etc. The third is the string design, including tension and planned use. The fourth relates to the bow, its quality and hair tension, etc.
It is entirely logical that lowering the string tension will allow the instrument to vibrate more freely and increase the flexibility of the strings. Is this leading towards trying to change the sound and response of your bass when at normal pitch? In other words, are you less than happy with your bass right now?
The simplest experiment to try first is with bow tension. The hair should gently bend over the strings in order to drive them without crushing their relative freedom to vibrate. If the hair is too slack the sound is too woolly and lacks projection. If too tight the stick feels too stiff and unresponsive, the hair will skid and note starts lack bite. Try tensioning your bow so that when at its middle you press down three strings at once by using your maximum usual weight. If you are a French Bow user (which I am) this will be when the hair also contacts the stick. German bow? Check out your note starts, all over the length of the hair and in both directions. Then increase hair tension in half-turn steps and try again each time. Repeat the process by lowering the tension in half-turn steps and experiment until you optimise the bow tension for your current strings and set-up. Your age of hair and brand of rosin are other considerations.
Still not happy? Then you embark on a careful process of adjustment and /or change. Do you have height adjusters on your bridge? Lowering your strings even slightly can change response. Or raising the saddle at the bottom of your tailpiece. These are not expensive changes. Probably the next step is sound post adjustment but beware of the affect of "soundpostitis"on your sanity. Experimenting with different strings can become very expensive as I'm sure you know. Changing neck angles or belly thicknesses are big expensive operations that are usually not warranted.
Best wishes, DP.