[Jim 9922]

While I am not a home watch service I am familiar with many service-type organizations. Normally "bonded" means that you would be covered for a dishonest act by an employee, such as theft of valuables, while checking the house, or coming back afterwards and stealing. Basically, bonded is "insuring" the "honesty" of the employees. "Insured" probably means they are insured against damage done by them or injuries incurred while on your property or carrying out their duties for you, which could also mean during their transportation to or from your house. Make sure they have coverage for both types of coverage (damages and workers compensation type of policies). You might be covered for "excessive" damage because they did not do a checkup during a promised rotation, or worse never checked, and faked reports that they did. Normal damage from breaking pipes, leaking roof, etc, or any other such thing is your responsibility and would be covered under a properly written home owner's policy.
There should be no hesitation by a business to show you a copy of a summary of insurance coverage being claimed to be in effect. Of course that is not 100% reliable in that policies can be terminated or canceled at any time without notice to you unless you are listed as "an additional insured party" or you are issued by the insurer a "notice demand of cancellation or non renewal" Notice demands are a bit extreme for this type of situation and is not usually done.
Hope this helps.