Learn to type in Pinyin for a Zhuyin user
There is an (almost) one-to-one mapping from Zhuyin to Pinyin, replacing symbols with letters. In my humble opinion, Pinyin only save one from remembering symbols.
Neither Pinyin nor Zhuyin is perfect. Better learn both of them.

Pinyin is the result of an attempt of romanization, everything is going well except that, after all, Chinese language is quite different from Latin family languages in many aspects, spelling, pronunciation, logic, or the way of thinking, so a perfectly matched mapping can be really hard to realize, if not impossible. So it's not surprising when the Pinyin transliteration is found to be a little strange to English pronunciation rules, e.g. in qi vs. chee, or gu vs. koo. A more intuitive transliteration is Wade-Giles. As a citizen of China, one had better learn and use Pinyin as Pinyin simplifies and boosts the learning or the input in digital devices in many situations. Chinese romanization is still in progress, and we all might contribute to it. Personally speaking, it is quite controversial to put Pinyin into the position of official representation of Chinese language pronunciation, say, for the lacking of cultural heritage, abrupt as a centaur. When it comes to input method, I prefer the faster heuristic Pinyin (such as Google's, QQ's and Sogou's) than Zhuyin.

Zhuyin, based on a system invented by the late philosopher 章太炎 in 1910's. Zhuyin symbols presents a concise representation, which implies a simplification of pronunciation patterns, in other words, a standardized Mandarin would prevail and dialects or variations had to fend for themselves. Zhuyin is still officially in use among Taiwanese people, some of which feel it hard to move to Pinyin, for many reasons, such as personal habit or belief. Say it practically, Zhuyin has some advantage: some vowel Zhuyin symbols may give less keyboard hits than Pinyin, e.g. ㄠ (L) vs. ao (AO).