I assume you want to collect the values of `c` in cList? 

Just replace your loop with

    cList=First@Last@Reap@While[Abs[b-a]/2>ϵ,
          c=(a+b)/2;
          iter=iter+1;(*number of iterations*)
          Sow[c];
          If[f[a]*f[c]<0,b=c,a=c]
    ];

![Mathematica graphics](https://i.sstatic.net/3MaBp.png)

Lookup help on `Sow` and `Reap`

Btw, `iter=iter+1` can be written as `iter++` in Mathematica.