I work in insurance in the US and strongly agree with the bolded. For information, the following applies in most states and for most policies in the US, but things vary by state and by company. Read your policy.

For a bicycle, you can get coverage in a number of ways.

1. For liability (damage you do to others) a renters or homeowners policy will cover this. Despite the damage occuring on the road, the exclusion is for motor vehicles. A bike is not a motor vehicle. The exception to this is electric bikes but I won't discuss them in a road bike thread.

2. For damage to your person...If you own an auto and have an insurance policy, you likely have some coverage for an accident with a vehicle. PIP (not all states) will cover you directly regardless of fault for your medical expenses resulting from a crash. If the person that hit you is at fault, and is not insured or is underinsured, Underinsured(UIM) and/or Uninsured (UM) will cover you (not your bike) in place of the other party's liability coverage. The other party's Bodily Injury and Physical Damage will cover damage to your person or bike if they are at fault.

3. Coverage from theft/vandalism ... Your renter's/owner's policy will cover you from theft/vandalism of your bike from your insured premesis. For additional premium, you can often schedule your bike and get coverage from theft/vandalism for locations other than your insured premesis.

4. Coverage to your bike due to damage in a crash. Pretty much the only way to get this is if the other party is at fault and has liability coverage. I'm not aware of any company offering collision like coverage on a non-motorized bicycle.