DMV's Reexamination Process, it appears that the revocation period is "indefinite" UNTIL certain conditions are met. As such, your question as to "how long before you are eligible to re-apply" will depend on the outcome of your hearing and is better directed at the DMV hearing officer you will meet with.
As for the 22349(a) "speeding citation", that carries one violation point and is indeed eligible for traffic school. You should receive a letter from the court confirming your eligibility for traffic school, and instructions on what you need to do to to enroll. You can contact the court clerk for more information about the fine amount, the traffic school administrative fee, and a list of traffic schools where you can take the class.