Not really. Jag kommer om en stund means that it will take a while before I'll be back. Like, prepare to wait. Not for very long, but for a while.
If you'd use moment in the English translation, you'd be saying you'd be back very soon, but that is not what the Swedish sentence means.
The main translation is I am coming in a while, this is a very good translation.
I am coming in a moment is not accepted because if you write that, you have probably misunderstood what the sentence is saying.
I am coming in a bit sounds vague to me, but as far as I can tell, it could probably mean I am coming in a while, so it is accepted too.
Do you mean to say that I am coming in a bit only means I will be there right away and thus also should not be accepted?
As a native English speaker, I'd disagree. "I am coming in a minute," is perhaps what you meant? But based on the exercises here, ett ögonblick is probably closer to "a minute" than en stund is -- and there are quite a few exercises here that try to enforce that distinction. Probably because ett ögonblick brings to mind the English expression "a blink of the eye", which is misleading because that's only used in English to refer to genuinely almost-instantaneous events.