You can use both App Bridge and Polaris at the same time. Polaris allows you to create UI elements inside your app iframe while App Bridge provides a way to render UI in Shopify Admin outside of your app. For example, when rendering a Banner inside your app you should use Polaris. For components that gets rendered outside your app iframe such as Modal, Toast and Title Bar, you would use App Bridge.
Currently, Polaris also provides access to App Bridge components but this is being deprecated in future release: https://polaris.shopify.com/components/structure/app-provider#section-initializing-the-shopify-app-b...
App Bridge is a vanilla JS library but it has React components released in a separate package: https://shopify.dev/tools/app-bridge/react-components
If your app is a React app, you should use Polaris (@shopify/polaris) alongside App Bridge React (@shopify/app-bridge-react).