How to safely clean tantalum jewelry
Ultra Met uses tantalum for corrosion resistant coatings and has a list of corrosive substances that won't dissolve tantalum, comprising of hydrochloric, hydrobromic, and hydroiodic acids, nitric acid, sulfuric acid, acetic acid, hydrogen sulfide and even pirahna.  

So unless you plan on using aqua regia, hydorfluoric acid, hot chlorine or other hot halogen gas, (none of which are safe for most metal jewelry) your ring should survive—at least the tantalum part will.