Do I need to disclose the bike citation if both citations were paid?

Read the instructions and questions on the application. If you feel uncomfortable, error on the side of disclosure. Also, consider hiring a competent and experienced immigration attorney in case there are other possible unknown complications, as well.

The naturalization application process requires each applicant to reveal all instances in which he/she was cited (or arrested or detained) by any enforcement officer for any reason. While some very minor offenses may have no consequences for naturalization eligibility, failure to identify them can form a basis for denial of a naturalization application. Appropriate certified copies of disposition documents should be supplied to the USCIS for each offense (and where no such documents still exist, as may be the case for a non-felony matter 12 years ago, an originally signed letter from the appropriate court representative explaining that no record exists and explaining why that is true, should be supplied). The naturalization application process often can be significantly more complex than it appears just from reading the Form N-400 and its instructions, and reading the statute and published regulations. Especially when an applicant has some "blemishes" on his/her record, it would be wise to work with an immigration attorney.