At this point, I do not think that anyone can really say for sure. However, the dimensions of the Staves of the Ark of The Covenant could be deduced from the original text. And hopefully, this will be accomplished in the near future.

Here is what I can say on this matter from my research:

1) Staves of the Ark were probably no longer than 10 cubits, as it had to fit inside the Holy of Hollies section of the Tabernacle. I think that 9 cubits is most reasonable number, although I may be mistaken. Here is how I render the Staves, so that there is some space left:

2) The Length of the Staves of the Ark also depends on how many people would be required to transport it. If it were 4 people, which is not unreasonable at all, then 9-10 cubits of length would be plenty to allow the Staves to cover the width of the Ark while leaving comfortable amount of space for 1 person on each side to carry it. Like so (shown without coverings):

3) Last but not least, there are plain engineering considerations as to what length the Staves of the Ark could have been. The Ark was relatively heavy, so the Staves had to be strong enough to be able to handle the load. Unfortunately it would be impossible for me, at least at this point, to perform even approximate calculations on this matter, but I can recommend to check out this article that should give you an idea of what is involved in this seemingly simple problem.

You can also check out this traditional article, and my Tabernacle Calculator if you want to play with your own numbers and see what you would come up with.

In my opinion, the only reasonable way to figure out the Length of the Staves of the Ark would be through logical reasoning based on the original text, so hopefully if I would be able to figure it out I would be able to post it here in the future.