There are two competing reactions you have to consider:
There is an acid-base reaction with litmus. Base colors it blue, acid colors it red. Maybe, you can write something like a reaction for this statement, using a common base and acid, for example, sodium hydroxide and sulfuric acid.
There is a bleaching reaction with, in your case, chloric acid. This is an oxidation, the large complicated organic compound litmus is destroyed by the bleaching agent. You can sort of write this one out as well, you can use any oxidizer, like permanganate, or something else.
You (and maybe your teacher) are making the problem little bit more difficult, you use the term bleaching for the pH color change and for the color loss. You should try to separate all the possibilities, to describe what really happens.