If you're in the incorporated limits of Bowie you'll be paying both a County property tax and a City of Bowie property tax. Your County rate will be a bit lower than than in unincorporated areas due to a tax differential granted the city to offset its costs for performing services, such as police, that are otherwiswe handled by the County.
You will be eligible for the Homestead Tax Credit after occupying the house for a year.
MD Current Tax Rates
Prince George's County, MD - Office of Finance : Treasury
Online Services
I didn't do the math but at your price of $325K the combined taxes you mentioned look a bit high, County will be about 3200 and Bowie will be about 1500. You may also have special assessments for trash service and water/sewer capital improvements billed on your tax bill.