They sound verrry similar - but, there is a subtle difference. (I'm talking about UK English. I'm from London.)
And subtle differences are important in poetry.
Bounce - ends with a softer 's' sound. Like the 's' in 'secular'.
Whereas, counts, having the 't' and 's' on the end, becomes that harder, more 'zzz' buzzy sound. Like the ts in 'tsar'.
I'd be a bit like 'er whar's that?' It would grate on my ear a bit.
I might, as a poet and songwriter, feel a bit short-changed, if presented with 'bounce' rhyming with 'counts' in a poem.
I'd feel more fulfilled if bounce rhymed with 'trounce', or 'pounce' or 'ounce'.
If 'counts' rhymed with 'amounts', 'founts' or 'mounts', I would also feel quite satisfied. But it depends...
Which word is best to use as a rhyme depends on the artistic work. You can get away with dodgy rhymes - if the words in the whole sentence and the words around it, hang together in a way that sounds pleasing to the ear. And/or is intetesting/makes sense.
Sometimes the use of a particular non,-fitting rhyme is humourous, or alludes to something else, mentioned earlier. Or has a double meaning. All of which can allow you to get away with it.
His countenance was just, but his hair was all mussed, as with a single bounced thrust, he undid his truss, 'for have you I must!: - the words burst out in a gust. .
And then, on all counts, in varied amounts, on dour countenances he bounced, the taxable amounts, as arguments were trounced, yielding... much poorer counts.
The 'counts' are noble Counts as well as 'sums of money' in my example.