Au conTRAIRE, mon frère! Insurance fraud is a HUGE enterprise with organized rings including body shops, doctors and attornies. But that’s a whole 'nother thread.
I would have to refer to my policy to see exactly what it may cover, but I do know that in many cases the coverage extends far beyond the end of my driveway. It is homeowner’s insurance, not house insurance, and it covers far more than the physical structure of the home.
There are already various means to insure against personal liability, medical, and damage/theft to/of your own personal property that such a unique type of insurance is unnecessary and would not be profitable for any US company to offer.
You’ve already looked. There’s nothing out there.
The only thing I can think of is Lloyd’s of London where I’ve heard they will insure practically anything - body parts of athletes and models come to mind. But I can’t imagine that would be at all practical/affordable for your situation.
In the US, most homeowners policies will cover your personal property anywhere in the world. There are exclusions and limitations to every policy so I would recommend that you either read yours or better call your agent to explain what coverages are available to you.
I’m not as familiar with liability coverages anymore so I can’t address the theoretical claim above with the bike rider running a stop sign. In general terms, the liability portion of the homeowners policy is there provide coverage for damages/injuries when the homeowner is negligent but there may be an exclusion or limitation for “vehicle” use that may include bicycles.
As others have said, talk to a professional agent to make sure your exposures are properly insured.
So a homeowner’s policy covers the insured for any negligent acts he might commit anywhere in the world (with the seeming exception of when driving a car)?
Basically, yes. Unless otherwise excluded. 
I’m working off of memory here but I think that it’s only your personal property that’s covered worldwide. I think the liability coverage is limited to the US and it’s territories. Then again, that may only be in the personal auto policy. I’d have to get off my arse and go look it up and I’m too lazy to go into the office tonight. To be sure, ask your agent.
The set of people in the US who use bicycles extensively as their primary transportation is quite small overall. The sub-set of people in that cohort riding bicycles expensive enough to be worth insuring is smaller still, and the sub-set of that cohort who would be willing to pay some amount to insure that bicycle instead of just taking their chances, and replacing it if necessary is vanishingly small.
Beyond this, given the high rates of bicycle theft in some areas (typically the areas of heaviest bicycle use) the cost of the premiums would likely be well beyond the perceived utility of the insurance.
It’s expensive for an insurer to set up new insurance plans, and to do so for a wafer thin cohort of prospects seems like a non-productive use of their limited resources.
Third party insurance for cyclists is not anything unusual at all, go to your broker and you can readily obtain a policy, it is very much worth having.
You can obviously get cover for loss or theft of your machine, there may be some conditions such as keeping it properly secured at work and at home - but that is not much differant to many other insurance policies.
If you join your national association, especially with a race licence, then you may find this covers third party liability - but you should get yourself some personal cover - you will probably be required to wear a crash hat.
Some folks here may have a thought that loss of a bicycle is not likely to be expensive, but $2000 is not even slightly unusual or all that much for a decetn machine, a second hand car may well have a lower value.
Make sure to get a ‘new for old’ policy.
Ignorance fought. I was under the impression that homeowner’s insurance only covered negligent acts in your home or yard.
So, if I leave my home in Key West, FL and travel to Nome, AK, and while on vacation there I throw a banana peel on the sidewalk, causing someone to slip and fall into traffic which causes the driver to swerve and run into a chicken truck full of nuns also carrying gold bullion from Ft. Knox and that chicken nun truck falls into a river and all people and property are lost causing financial catastrophe unknown to human existence up until that point, I am covered up to my limit? 