Your standard homeowners insurance DOES NOT cover your bike if you wreck it regardless whose at fault. Only a floater or a rider for that bicycle would cover for such an event. If the wreck isn't your fault and the other person was driving a car their insurance would cover your bike, otherwise without a rider you're screwed. However read my previous post about why I don't have a rider on my bikes.

And yes you do have responsibilities to properly securing the bike in order for your standard homeowners policy to cover you for theft. Again read my earlier post.

I may put a rider on my touring bike when I do my trip across America, just to make sure the bike is covered in case something happens, but once I'm done touring I'll remove it. But I still have 8 to 10 years before I retire and do the trip.

I know my earlier post is long but there's good info in it. If something is not correct in it I'm sure someone will correct it, but I think to the best of my limited knowledge that is mostly correct.