Bed time

Yes, the phrase "9:30 bed time" is natural English. This is a short version of saying "My usual bed time is at 9:30". The way it's worded makes it clear that 9:30 is the standard time at which someone goes to bed. This phrasing is particularly common in informal speech, and you're likely to see it in contexts such as YouTube videos, casual conversations, or social media posts.

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Do you say “I go to sleep 9:30 today” when you do not have a bed cause you’re camping outside?
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The phrase you've written is understandable, but it's not the common way native English speakers would likely express it. Instead, they would probably say something like "I'm going to bed at 9:30 today," even if they were camping and there wasn't an actual bed involved. The phrase “going to bed” doesn't always literally mean going to a physical bed; it often simply means going to sleep.

So, you could say "I'm going to sleep at 9:30 tonight," or "I'll be hitting the hay at 9:30 tonight," if you want to convey that. 'Hitting the hay' is an idiomatic expression and it also means going to sleep. It's pretty informal and generally used in casual contexts.

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I don’t have a bed to sleep _____

What word should be placed in the blank?

"In" would be the best word to complete your sentence.

Here's the corrected sentence: "I don’t have a bed to sleep in."

This sentence means that you currently do not possess a bed that you can use for the purpose of sleeping.
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In the sentence “on” is not appropriate?
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Correct, "on" is not the standard preposition used in this context in English. While it is true that physically we sleep "on" a bed, the phrase "to sleep in" is the established idiom in English. It encompasses the idea of being in bed, covered with blankets, and not merely on top of the bed. However, if you are talking about just lying down or resting on top of the bed without necessarily sleeping, then you could say "I don't have a bed to lie on".