What insurance options, if any, exist to allow an individual to transport valuable items owned by others with minimal liability?

I would suggest Alice and Bob talk to their lawyers. What is needed here may simply be a contract stating that while Bob shall exercise due diligence, Bob is not responsible for any loss or damage while the object is in his care. Note that Alice can still try to sue Bob, but if phrased properly this should prevent such a suit from succeeding unless Alice can show gross negligence or deliberate malfeasance.

If Alice wants the object insured while in transit, I think it's Alice's responsibility to find suitable insurance.Note that if Alice was carrying it she might still want to ensure it. Bob isn't the only one who might have an accident.

(I carry an umbrella policy that explicitly covers specific equipment that I sometimes travel with and that would be hard to replace. I believe that insurance applies whether the object is in my hands or not. There may be a cheaper way to do it; I presume there are policies specifically for folks like touring artists. Some variant of travel insurance, perhaps. The insurance agent should be able to find something suitable. If not, find another agent.)

...how can Bob insure these against damage or theft in transit, and prevent Alice's insurance company from attempting to recover the loss by suing Bob? (Even if Alice and Bob are friends, insurance companies tend to be amoral so there seems to be a risk this could happen even if Alice does not want it to.

By buying insurance...

There are dozens of insurance companies that cover fine art and other things of extreme value. There are far more insurance companies that sell liability policies to businesses dealing with high value items. To limit individual liability businesses use LLC/corporations. Anyone hiring the business for something involving items of extreme value should ensure that the business's insurance coverage is adequate and/or ensure their coverage will act as secondary if business coverage is lacking.

Insurers will evaluate value of items and assess the risk of loss based on the activity/situation, then charge premiums that are likely to result in profit.

If some random person wants to haul a billion dollars of art in a trailer across the country, the premiums would be incredible if any insurer was even willing to take on that risk. Professional services carry liability insurance to cover themselves and achieve lower premiums by establishing track record of trustworthiness and risk-mitigating practices (like not packing a billion dollars worth of art into a single uhaul).

You may find that the convenience of Bob shlepping things around is more than offset by the costs to insure the items. If you are Bob, then you want create an LLC to protect your assets and ensure that your liability coverage is adequate. If this is just a friend doing a favor, then you need to ensure Alice's insurance covers the situation you have in mind.

There doesn't seem to be a country tag attached, so I will answer for netherlands.

In The Netherlands, an individual takes on a (recommended by the government, not mandatory) liability insurance, which usually covers incidents up to 1.2M EUR (I have even seen insurances up to 2.5M EUR).

This is called an Aansprakelijkheidsvezekering. It covers damage for exactly this situation, where you offer to help a friend but due to offering help to your friend you unintentionally damage, break or destroy something, then the insurance will cover that cost.

Personal Liability insurance does not cover act of business, for that a separate business liability insurance is needed.