One of the origin story of the term links to a once-popular Hong Kong actress Amy Yip[1], who was known for her cup size and sexy appearances in movies. The "nickname" 波霸, roughly translated to "Boobs overlord" in English, or transliterated to "Boba" (sounds similar in both Cantonese and Mandarin), was given to her by the media.

It was said that one bubble tea maker in Taiwan made large tapioca bubbles to put in milk tea, when tiny bubbles were used in milk tea at the time, and he named it "Boba tea", associating the relatively huge size of his bubbles with the actress well-known body feature. https://en.wikipedia.org/wiki/Amy_Yip