Learn Hardcore Arabic (Modern Standard): بعد ساعة أعود إلى البيت.

Literally, بعد ساعة means “after an hour.” In everyday usage, it often functions like English “in an hour (from now)”—i.e., after one hour has passed starting now. If you want to be extra explicit, you can say بعد ساعة من الآن (“an hour from now”).

Why is it ساعة (singular) and not ساعات (plural)?

Arabic commonly uses the singular for measured time spans when the number is one or when it’s understood as a single unit: ساعة = an hour.
If you mean two hours, you’d typically say بعد ساعتين. If you mean three+ hours, you’d use the plural with a number: بعد ثلاث ساعات.

What case should ساعة be in after بعد?

In fully vowelled Modern Standard Arabic, the noun after بعد is normally genitive (majrūr) because بعد behaves like a time adverb that takes an annexed noun:
بعدَ ساعةٍ
So you may see بعد ساعةٍ with tanwīn kasra in careful writing. In unvowelled text (most normal writing), it appears as بعد ساعة.

Why is the verb أعود in the present tense if the meaning is future?