Michael is right tha $1,000 is not considered a high tax bill in most areas, and gave good information on how the taxes are figured.. I know that is little consolation if that is an increase over what she has budgeted.
There may be a Homestead Exemption that would reduce the tax burden for your grandmother. More and more areas are setting a threshhold of value that a resident homeowner has an exemption for, when computing the taxes. This helps to offset those rising tax bills for seniors and others. Check with your county tax office or local school officials.
May I offer some additional input? Another thing to keep in mind is that while your grandmother may not have anyone currently in school system, she probably is the beneficiary of some programs that other taxpayers are carrying the financial burben for. That is the way tax structures work to provide services for us all--not on a pay as you use them basis.
Hope that helps