Just use sodium cholate or dissolve your cholic acid in NaOH or directly dissolve it in your cell culture medium if your final concentration is less than 0.2 mM or dissolve it in acetic acid (unless you consider it as an organic solvent) or ...
My advice is prepare a concentrated stock in which you use tricks to dissolve it (such as the 1N NaOH) and then filter it and aliquot it, storing all the aliquots but the one you will use for this particular batch of media in the -80C. When preparing your media you add the required amount of your cholate stock and then you adjust the media pH to 7.4. If you prepare more media within the week you can use the same aliquot if you take more than a week then I would defrost a new aliquot and repeat.