Attorneys who work in criminal law cases without being paid by their clients are public defenders. If your income meets the local requirements for government-paid legal representation, you likely can ask for a public defender. You may have to fill out some application and provide proofs of income.
Besides public defenders, you likely will not find any attorney to represent you in a DUI case for free. Defending a DUI defendant usually does not result in any public good.
If you are confusing "pro bono publico" with "on contingency", you should be aware that in most (if not all) states, attorney's fees that are contingent on the outcome of a case are prohibited in criminal law cases and family law cases.
On the other hand, each attorney generally has the right to decide what cases the attorney takes. You can call several law offices in your area and find if anyone will take your case.
DUI attorneys are essentially criminal defense attorneys. You may qualify for public defender representation in your case if you have a low enough income. In that case, you get whoever is assigned to your case. The person may not know much about DUI or they may be an expert. It is the luck of the draw. The best way to go is to hire your own attorney with a track record of fighting DUI cases. That is the best way to ensure that you will get a proper defense.
If you were charged in Cobb County, you could qualify for a circuit defender if your income qualifies. We have many experienced DUI attorneys in Cobb. Cobb County has the largest amount of DUI arrests in the State of Georgia. On July 1st of this year the DUI law changed in Georgia which has significantly increased the long term consequences of a conviction. Hiring an experienced DUI attorney to assist you in your defense will be money very well spent. At your first court date you can inquire about a circuit defender. You do not get to chose your counsel that way.