Think of the word as three pieces stuck together: bi (two), week, and the -ly that turns it into a description. What the pieces never settle is what the two counts. Two weeks between one thing and the next? Or two of them inside one week? Both readings are alive, and the word will not choose for you. So the useful picture is not a calendar — it is a question mark over the number two. Good writing answers that question by naming the days.
From the word’s history
Wiktionary records the word as bi- + week + -ly, and adds that the twice-a-week reading can be analysed instead as bi- + weekly. The two possible splits of the same string are exactly where the two meanings come from.
Wiktionary 記錄這個字來自 bi-（二）加 week（週）加 -ly。它同時指出，「一週兩次」那個意思可以拆成 bi- 加 weekly。同一串字母有兩種拆法，兩個意思就是從這裡分出來的。這不是後人硬湊的巧合，而是構詞本身就留下的縫隙。
Wiktionary, "biweekly"
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