The burden of proof is in the hands of the accuse; it is commun that tax payers end up having huge fines when they didn't cheat or broke the law
The fact that it was not intentional may be considered attenuating circumstance in some cases but it will not save you of paying some fines
In order for them to initiate a audit they must have some evidence that fraud occurred.
The "evidence" can come from MANY sources, but there must be a discrepancy in your taxes.
They will not simply audit random people who may or may not have bought/sold bitcoins. If you were intelligent enough to trade your bitcoins in a pseudo-anonymous format, they will never know.
That all said, if they have some evidence you have been dealing in bitcoins that you never reported, you will likely be audited, and you will have to prove that you have never traded bitcoins.
This is not true. If you avoid exercising any federal privilege in your bitcoin dealings, then you have no obligation to report them. An analysis of Title 26 demonstrating this pretty clearly (and proving it with evidence from the IRS and Treasury) is available at losthorizons.com.