Your taxes owed under any of the posted tax rates can be calculated as follows:

Tax Rate x Net Taxable Value ÷ $100 = Tax Bill

Proposed Average Residential Tax Bill: .520000 Tax Rate x $186,173 Taxable Value ÷ $100 = $968.10 Tax Bill
Average Residental Tax Bill (2016): $0.476509 Tax Rate x $168,609 Taxable Value ÷ $100 = $804.44 Tax Bill

This represents an Average Residental Tax Bill increase of $164.66 or 20.49%

Senior Tax Freeze

In 2004, the City of Bedford adopted an ordinance that establishes an ad valorem tax limitation, otherwise known as a Senior Tax Freeze, for homeowners age 65 years or over and their spouses, in accordance with the Texas Constitution and the Texas Tax Code

For property tax accounts that have an 'Over-65' exemption, your Tax Bill is capped at a maximum amount.
This simply means should the City of Bedford adopt a tax rate that exceeds the prior year's tax rate, or if your taxable value exceeds the prior year's value, it will have NO EFFECT on an Over-65 Tax Bill. That particular tax bill will remain unchanged from the year that bill initially qualified for the Senior Tax Freeze.
For example, here's a sample an Over-65 Tax Bill that is capped at $425.00:

YEAR 1 - $0.476509 Tax Rate X $89,190 Taxable Value ÷ $100 = $425.00
YEAR 2 - $0.520000 Tax Rate X $95,000 Taxable Value ÷ $100 = $494.00 $425.00 (capped)