How to use the new @Shopify/app-bridge with @Shopify/polaris-react

Shopify recently released their new @shopify/app-bridge, but it is unclear to me how it should be used alongside @shopify/polaris.

For example, I have tried to make a React component that will use the app-bridge and polaris to display a toast.

import React, { Component } from "react";
import * as PropTypes from "prop-types";
import { Toast } from "@shopify/app-bridge/actions";
import { Page } from "@shopify/polaris";

class Start extends Component {
  static contextTypes = {
    polaris: PropTypes.object
  };

  showToast() {
    console.log("SHOW TOAST");
    console.log(this.context.polaris.appBridge);
    const toastNotice = Toast.create(this.context.polaris.appBridge, {
      message: "Test Toast",
      duration: 5000
    });
    toastNotice.dispatch(Toast.Action.SHOW);
  }

  render() {
    this.showToast();
    return (
      <Page title="Do you see toast?">
        <p>I do not see toast.</p>
      </Page>
    );
  }
}

export default Start;

But it does not seem to dispatch the action. Any ideas on why not? Note that my app is wrapped in the AppProvider and app-bridge is initialized.

ReactDOM.render(
  <AppProvider
    apiKey={process.env.REACT_APP_SHOPIFY_API_KEY}
    shopOrigin={queryString.parse(window.location.search).shop}
  >
    <Start />
  </AppProvider>,
  document.getElementById("root")
);

Any suggestions?