You want what's called a "combo amp". It features an amp head section that you plug your bass straight in, attached to the top of a speaker cabinet. There should be some decent Ashdown or Trace Elliot combo amps on the used market in your area.
A PA is typically a mixer, an amplifier, and a set of full-range speakers. Many of them have the ability to take an instrument signal straight in, but not all of them work well that way. Also sometimes a PA unit is sold without speakers, so be sure what's included in the price. You're probably better off looking for a bass-specific combo amp.