The hard answer is that you'll need to rephrase it as an indirect question.

"When is dinner?" Bob asked > Bob asked when dinner would be.

To rephrase this even more, a final translation might look like: Bob ruz laan do tiid se kipraan "Bob then asked about the time of the meal."

The storytelling that we've seen in Dovahzul doesn't make use of direct question or statements. The obvious difference between English and Dovahzul is that Dovahzul lacks any form of punctuation to indicate this.

Well we added punctuation in dovahzul for period, comma, question mark, and exclamation points. So why not add in quotations, at least for a modern usage? 

I actually have considered this. I thought of making the runes much like how they are in english.

I disagree, and think that our invented punctuation should actually be phased out. It doesn't fit the spirit of the language and goes against canon for the sake of making it more like English.

I get that and I don't mind not having punctuation I just think there should a way of quoting someone in Dovahzul. They don't even need to be "quotes" (heh) but maybe a symbol of sorts just to say "this a quote" or "this is exactaly what was said" with out having to say "this is exactaly what was said". If having punctuation is too much then why not just exclude "that"? For example it would be basicly an inderect statement/question with out "that" and an inderect statment/question would have a "that". Would that work better as a standered? If you have "x said y" it is a "quote" and if you have "x said that y said z"  then it would be inderect.

This is a very good question, that I've actually tried to solve on my own, in my currently-halted Alice in Wonderland translation project. In this project, I opted not to use punctuation, but instead to use line breaks to infer new ideas, as is most similar to word-walls. However, this is a very big challenge, especially with dialogue (direct quotes). I tried to just infer the meaning (abridge it a little for the sake of the language), but this is used only in the minority of dialogue. Here's how I went about translating direct quotes as direct quotes:

Take this sample:

"Well!" thought Alice to herself, "after such a fall as this, I shall think nothing of tumbling down stairs! How brave they'll all think me at home! Why, I wouldn't say anything about it, even if I fell off the top of the house!" (Which was very likely true.)

I translated it as such:

alis lorot
ful! mindin mah med daar mah tum stegniir los nid
nust koraav zey kril ahst hofkiin
saag nid waan mah nol hofkah tol lost lot grozein vahzah

Notice how the first line in the quoted paragraph indicates the person speaking, as well as defining what he/she is doing to produce the quote (says/thinks). And to end the quote, a double line-break is used to show separation (as I do with each new paragrah, though the Dragon-Tongue paragraphs don't match up to English paragraphs because paragraphs in Dragon-Tongue are shorter, so there is oft multiple Dragon paragraphs per English paragraph).

This isn't quite a cononical way to do it, but it's the closest that we're going to get.

EDIT: I forgot, I do use punctutation, but only exclaimation marks.