You might not be able to "beat" it, especially with an injured bicyclist and your turn signal not working. You have good reason to be concerned about liability. Hire an attorney and don't talk with anyone except the attorney about your case.
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Based on what you have said, I'm somewhat surprised that you were not charged with careless driving causing bodily injury. You have some potential issues to be concerned about regarding liability if the injured bicyclist decides to get a personal injury attorney. You should consider hiring an attorney to assist you with the traffic citation and to help you with any attempt at the DA's office to amend charges and potentially reserve restitution. Mr. Leroi would be a wise choice as your attorney.
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Given your facts, I see little to no way this will get dismissed. The rider will be compensated and you should contact an attorney to see about options to get this reduced.
This answer is for informational purposes only and is not legal advice regarding your question and does not establish an attorney-client relationship.