How well is pinyin known in Taiwan? I've been using pinyin in my study, but a Taiwanese co-worker recently arrived.  I see that Taiwan only made pinyin official in 2009, so I wonder how likely she is to have mastered pinyin, having finished college before 2009.  I do know that at least one university there uses pinyin.

Of course I can ask, but I don't know how reliable her self-assessment will be.  I wouldn't mind learning bopomofo, but I don't want it to slow down my learning to actually speak.
Not very well known. I lived in Taiwan for a year in 2015, and there were times where I had asked a few Taiwan natives to type words I couldn't understand on my phone. When they saw my phone keyboard input, which was pinyin, they couldn't understand it. Almost all Taiwanese still use bopomofo to type Chinese on their phones. Honestly you don't have to learn bopomofo. Pinyin is easier to learn and the majority of Chinese speakers use it. Just focus on using pinyin, memorizing characters, and speaking to Chinese speakers.