car repair reimbursement

Hello, Good evening po sa lahat! I am contemplating on what action should I take against a bus company which as of the moment, fails to reimburse me of the expenses I incurred in the repair of my car bumped by one of their buses.
In the police investigation, it clearly appeared who was at fault in the car collision from which both of us were involved, and that's them. When we were at the police station, it is agreed upon by us, both parties, to settle the expenses for the repair of my car from their "supposed" insurance and so with that, the bus was released and continued its travel.
Later then, I found out that their units were not covered by any insurance policy, as they have none. The management of the bus company then urged me to let the repair done in their own repair shop, however I declined from their offer because I wanted to make sure that the repair would be at the best of my interest (who knows, they might just do the repair for the sake of claiming that they have already done their part in fulfilling their obligation). I had the second thought of handing them over my car because the location of their shop would not permit me to do the regular checking, as it is far from my home and workplace. Several talks and bargaining transpired and then we agreed to just lower the cost that they are going to pay me as against that of the repair estimate done in one of the repair shops near the police station. Because of that, and with much excitement, I immediately decided to just bear the cost of repair for the meantime and later reimburse all the expenses incurred.
Now that my car is all done, they are already ignoring my demand. Phone calls and text messages were completely ignored by them, and so as of now, I am already pissed chasing them extrajudicially. The incident transpired for over a month now and I have incurred much damages from their inaction. The inconvenience brought by them is no longer amusing, definitely not.
Can you please, Sir, help me with this? I would appreciate very much, whatever kind of help you may extend. Thank you!.

Did you take pictures of the damaged portion of your car before you have it repaired? Just in case it goes to court, its a proof plus the receipts. Do you have insurance for your car? If yes, you can just file your own damage claim with your insurer, and its the insurnace who will run after the bus co. If you don't have, and the bus company keeps on ignoring you, send them a demand letter with warning of suing them in court. If they still don't pay then sue them.

Thanks for the reply.. I have all the pics taken at the scene with me, a copy of the investigation report and a photocopy of the police blotter where our agreement was recorded. No, my car is not insured.

Is it required that the demand letter be in a certain format, and do I need to avail the service of a lawyer to draft it for me? Thanks again Sir/Ma'am.

What may be the possible charge/s to file should I decide to bring this matter in court? Thank you..

Reckless imprudence resulting to damage to property plus damages.

Thank you Atty. I have talked to one of their representatives over the phone just a while ago and made the same demand. She actually told me that they are already processing the documents required for the release of their money to cover my expenses. Instead of having that sigh of relief from that response, I felt irritated because that is still the same answer they are giving me everytime I communicate with them. What's worst was that when I asked her, "Kailan naman kaya maire-release yan, next year?" and she sarcastically replied, "Hindi naman siguro, mga 8 years lang". I think that is already too much..

Now, I would want to ask how can I fixed the term or period of the payment? Would their statement, "We are already processing the documents" be a good defense for them to claim that they are not escaping from their liability? Thank you!