I sorta disagree with the argument that it is the insurance company's obligation to gather up the estimates. If you're the guy asking for money, it is your obligation to tell them how much you want, and give them written documentation backing up your demand. Otherwise they will just pay you what they want, when they want. Generally insurance companies make an initial determination of whether a piece of property is a "total loss" or "repairable". Using this same theory and assuming your bike is not repairable, then I still suspect that rather than cutting a check for full value of the bike, I bet they try and nickle and dime you to death by deducting for anything salvageable from the bike, e.g. non damaged seat, etc. Also, watch out for "replacement value" versus "fair market value". Insurance companies know that "used" property does not have the same value as it once did when it was sitting new on the show room floor.
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Two wheels good. Four wheels bad.