The US immigration authorities don't have direct access to UK criminal records (although the US government continues to press for such access). The chances are that, if you break the rules and enter under the Visa Waiver Program, you'll get way with it. (The UK authorities do pass some information to the US. For security reasons, they won't say exactly what this includes but it's unlikely that a DD conviction would show up).
If you do try to enter the US under the Visa Waiver Program, and get found out, you will probably be refused entry. You will then either have to fly back on the first available flight (at your own expense - which might mean paying a top-price fare with a full-fare carrier) or be held in a detention facility (effectively in jail) until your booked return flight. As I've already stated, it's unlikely that the US authorities would find out about your conviction but it's important that you should know what might happen if they do.
To complicate matters however, there's an apparent discrepancy over US immigration rules. The US embassy website makes it clear that any arrest or conviction (apart from minor non-arrestable motoring offences) bars you from entering the USA under the Visa Waiver Program. The actual question on the visa waiver form though, only asks about offences 'of moral turpitude'. It seems that you could answer 'no' to this question without lying.
As I originally stated, you probably won't have any problems entering the US. However, if it's going to worry you, you can go through the lengthy (5 to 6 months) visa application procedure. Details are in my post, here:
http://www.theanswerbank.co.uk/Travel/Question 289769.html
Chris