This is a difficult question to answer because there is not a single, fixed price that every attorney charges. You probably already knew that but that's about all I can really tell you. I would recommend using this site to find a few a traffic attorneys and contacting them and asking of them directly about their rates. Just be cognizant and respectful of their time and you should have good luck finding someone!
This is NOT legal advice. No attorney-client relationship exists.
You should hire a lawyer. a good traffic lawyer may be able to get the case dismissed and/or lower fine so that the increase in insurance does not happen. Make the cop prove his case.
Feel free to contact us for a consultation. Iannelli & Associates, 949 729-3171 This answer does not constitute legal advice and no attorney client relationship is created. Every case has many facts which are different and distinctly theirs, make sure that you understand this is general information and it would be advisable to constact a competent lawyer for personal legal advice.