Can I change the wording customers see?

Yes. Customer-facing wording lives on the bundle block in your theme editor — the add-to-cart button, the progress note (“add 2 more to save 15%”), the gift picker heading, the empty state, and more all have text settings, and leaving one empty uses the built-in wording. Two things are set per campaign instead: the bundle's name in the cart (in the campaign's Basics) and each discount step's own message and badge.