If the bicycle can be repaired for less than its market value, whatever you pay for repairs is your claim for property damage. Some insurance companies have expedited claims processes, but those are in the minority, so you generally should not depend on getting paid quickly from the insurance company.
Things get a little more difficult when the bicycle is totaled. In such an instance you are not generally entitled to recover the full amount of the cost of a brand new bicycle. Illinois law allows a person to recover the cost to repair the property or the property’s reasonable market value at the time it was damaged, whichever is less. Insurance companies will generally take the value of your bicycle purchased new and depreciate it based on its age and use history to determine what amount they will pay voluntarily. The reasonable market value of a bicycle can be established through testimony of an experienced bicycle salesman/mechanic who has knowledge of local market prices for comparable bicycles.
Take pictures of the bicycle. I generally think it’s a good idea to take pictures that show the whole bicycle from the drivetrain side. You’ll want to take close-up pictures of any specific areas that are damaged.
You should have one or more damage estimates performed at bike shops. Bike shops do this type of thing in the regular course of their business, and there is often no charge. Sometimes the shop will point out damage that you didn't notice initially. Take more photos if you need to better document additional damage.
The insurance company will typically ask for the original purchase receipt, so dig it up if you still have it. Insurance companies use the purchase receipt as a place from which to start depreciation calculations to estimate current market value of the bicycle. Sometimes it makes it harder for them to haggle over the bicycle’s value, especially if you paid full price for the bicycle.
You’ll need to call the insurance company and open a claim. Find out to whom you should send the materials relevant to your property damage claim. Keep the claim number handy. You should reference that claim number every time you call the insurance company. Before you have any repairs performed you may want to offer to make the bicycle available for the insurance company to inspect.
Once you have all the relevant documents collected you should send them to the insurance adjuster. It is reasonable to expect a response within 60 days to let you know whether or not they will pay your claim, or if they need further information. If not, it may be necessary to follow up with them yourself. If they flat refuse to give you an answer you may contact your state department of insurance to determine if there are grounds to file a complaint for vexatious refusal to acknowledge your claim.
If the insurance company ignores you, tries to low-ball you, denies your claim, or if the driver is uninsured and refuses to pay out-of-pocket, you can file a lawsuit. This is your final trump card. Every citizen has a right to have their grievance heard in court. In Illinois there are special “small claims” courts meant for people with cases that might not warrant hiring a lawyer. Small claims courts are generally more informal and often have relaxed rules of evidence to make it easier for people to seek legal relief without the need to be represented by an attorney. In Chicago you can file your small claim on the 6th floor of the Daley Center.