As dartme1 writes, this appears in Biblical Hebrew and in 100+ years old literary Hebrew. Doesn't work in spoken Hebrew in present and in future tenses; you do need the pronoun. Strangely, the pronoun is omitted in the past: "למה בהית בי?" (Also in declarative, BTW: "בהית בי."), and added only to stress - "למה אתה בהית בי" would be used only if stressing אתה, to mean "Why did you, of all people, stare at me?".
It can be understood why the pronoun is required in present tense - the verb form is much less specific. I'm not sure why the difference between past and future, both are about as specific.
I only know ancient Hebrew. Ancient Hebrew regularly uses inflected verbs and no pronouns. So far in Duolingo, I don't think I've seen any perfect or imperfect inflection. What you wrote might be translated: Why is [there] one staring at me? (though this shoresh wasn't used back then to my knowledge.) lamah יִבְהֶה bi? is "Why will he stare at me?" lamah בָּהָה bi? is "Why was he staring at me?" and different verbs for feminine.
Taken from https://www.pealim.com/dict/181-livhot/