Full Disclosure: I am not a proponent of bleach. Others on this site are and I'll leave it to them to expound on the best practices for using that product.
Most liquid chlorines have a shelf life of only 90 days or so, and the more the bottle is jostled, the more gas is generated and released. This lessens the effect of said product. Additionally- Bleach burns off rather quickly. Thus- You have two things working against you as it pertains to chlorine loss. I'd say its one of these two factors that have caused your low chlorine readings. Other things could be you put in too low of a dose, your testing equipment is bad or mis-fired, etc.
Di-Chlor is how I go if I do standard chlorine. There is a very recent thread you should search for on this site pertaining to bleach / Di-Chlor and it may help better explain the pros and cons of each. Regardless of what I think, the most important thing for you to do is to find a sanitation method that works for you and keeps your tub safe and clean, w/o damaging parts.
I hope this helps. Good luck moving forward.