#JavaScript (ES6), 126 <s>141</s>

A porting to javascript of the Pip answer by @DLosc. I needed some time to fully understand it, and it's genius.

**Edit** -15 bytes following the hint by @Titus, directly appending chars to the input string `a` and avoiding early return (so no `for/if`)

Assuming lowercase input

<!-- language: lang-js -->

    a=>[...a].some(z=>c(a+=z)>b,c=a=>(k={},a.replace(/[cowbel]/g,x=>k[x]=-~k[x]),k.l>>=1,Math.min(...Object.values(k))),b=c(a))&&a

*Less golfed*

<!-- language: lang-js -->

    a=>{
      c=a=>( // cowbell functions - count cowbells
        k={},
        a.replace(/[cowbel]/g, x => k[x] = -~k[x]),
        k.l >>= 1,
        Math.min(...Object.values(k))
      );
      b = c(a); // starting number of cowbells
      [...a].some(z => ( // iterate for all chars of a until true
        a += z,
        c(a) > b // exit when I have more cowbells
      ));
      return a;
    }

**Test**

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

    f=a=>[...a].some(z=>c(a+=z)>b,c=a=>(k={},a.replace(/[cowbel]/g,x=>k[x]=-~k[x]),k.l>>=1,Math.min(...Object.values(k))),b=c(a))&&a
      


    ;["christopher walken begs for more cowbell!"
    ,"the quick brown fox jumps over the lazy dog"
    ,"cowbell"
    ,"cowbell cowbell cowbell"
    ,"cowbell cowbell cowbel"
    ,"bcelow"
    ,"abcdefghijklmnopqrstuvwxyz"
    ,"cccowwwwbbeeeeelllll"
    ,"be well, programming puzzles & code golf"
    ,"lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. wow!"
    ,`c-c-b-c
     
    i have a cow, i have a bell.
    uh! bell-cow!
    i have a cow, i have a cowbell.
    uh! cowbell-cow!
     
    bell-cow, cowbell-cow.
    uh! cow-cowbell-bell-cow.
    cow-cowbell-bell-cow!
    `].forEach(x=>console.log(x+'\n\n'+f(x)))

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