Learn Farsi: شما باید به بیمارستان بروید.

This is the present subjunctive form! In Farsi, when you use words like bayad (must/should), the main verb that follows must be in the subjunctive. We form this by adding the prefix be- to the present stem of the verb. For the verb raftan (to go), the present stem is rav, giving us be- + rav + -id (the ending for "you") to make beravid.

Does the word bayad (must) change its ending to match shoma (you)?

No, it doesn't! Bayad is an impersonal word in Farsi, which means it stays exactly the same no matter who is doing the action (I, you, they, etc.). Only the second verb (beravid) takes the personal ending to match the subject.

How would beravid sound in everyday spoken Farsi?

In conversational Farsi, the present stem rav often shortens, and the formal "you" ending -id usually changes to -in. Because of this, you will almost always hear native speakers say berin instead of the written form beravid.

Do I have to use the preposition be (to) before bimarestan (hospital)?

In formal written Farsi, yes. However, in casual spoken Farsi, the preposition be is very often dropped when going to a destination. It is perfectly natural to hear people say shoma bayad bimarestan berin.