Is it correct and natural to use both the present simple and the present continuous for future scheduled events? For example:
I go home tomorrow at 4pm.
I'm going home tomorrow at 4pm.
By that I mean that my bus leaves at 4pm.
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There's a slight nuance of difference in that OP's first (present simple) version tends to imply "by arrangement" - often meaning the speaker is somehow constrained / obliged to carry out the "planned" future action (a plan perhaps enforced by someone else, or by circumstances).
The second (present continuous) phrasing is more common anyway (the first is a bit "formal / literary"), but it also more naturally carries the implication that speaker will be acting of his own free will.
Note that this semantic distinction is only a tendency - it doesn't always apply. For most purposes the two are equivalent in meaning (but the first version would usually be recognized as slightly "stiff / starchy" phrasing).
Using the simple present to describe a future activity usually implies that that activity is happening according to a schedule, as is the case in your first example sentence. So your first sentence roughly means, "I am scheduled to go home tomorrow at 4", and it also implies that you intend to follow that schedule.
The second sentence simply declares that you're going to leave tomorrow at 4 with no other nuance.