That's not what bounded accuracy is. Bounded accuracy is only the rule (guideline, really) that you'll never add more than a fixed value (+20, I think) to a d20 roll. It is not about damage, HP, or how many d20s you roll.
HP and damage are free to scale, but the d20 modifiers are not.
https://www.dandwiki.com/wiki/Understanding_Bounded_Accuracy_(5e_Guideline) is a good summary. The developer's own words section is also detailed.