gist showing Admob Banner Ad use within react native. It's not perfect, but it works. Not included: build.gradle which needs dependency on play-services-ads.

AndroidAdMobView.js

var { PropTypes, requireNativeComponent } = require('react-native');
var React = require('react-native')

var {
		StyleSheet,
		View,
} = React;

var iface = {
		name: 'AdmobView',
		propTypes : {
				pubId: React.PropTypes.string,
			loadAd: React.PropTypes.bool,
			renderToHardwareTextureAndroid: React.PropTypes.bool,
				onLayout: React.PropTypes.func,
			importantForAccessibility: React.PropTypes.bool,
			accessibilityLiveRegion: React.PropTypes.string,
			accessibilityComponentType: React.PropTypes.string,
			accessibilityLabel: React.PropTypes.string,
			testID: React.PropTypes.string,
		}
}
const AdMobView = requireNativeComponent('RCTAdmobView', iface);

var AdUnit = React.createClass({
		propTypes: {
				pubId : React.PropTypes.string,
		},

		getInitialState: function() {
				return {
						rendered : false, 
				};
		},
		componentDidMount : function() {
				this.setState({
						rendered : true, 
				});
		},
		render: function() {
				return (
								<View collapsable={false} style={styles.adcontainer}>
								<AdMobView ref="adView" style={styles.ad} pubId={this.props.pubId} >
								</AdMobView>
						</View>);
				},
});

var styles = StyleSheet.create({
		adcontainer: {
				minWidth: 320,
			minHeight: 50,
				width: 320,
				height: 50,
				backgroundColor: '#CCCCCC',
		},
				ad: {
				minWidth: 320,
			minHeight: 50,
				width: 320,
				height: 50,
				backgroundColor: '#CCCCCC',
				},
})

module.exports = AdUnit

index.android.js

'use strict';

var React = require('react-native');
var {
  AppRegistry,
  StyleSheet,
  Text,
  View,
		Dimensions,
} = React;

var AdUnit = require('./AndroidAdmobView');
		
var admobe = React.createClass({
		render: function() {
		  // pubId below is test pub ID for banner ads per https://developers.google.com/admob/android/quick-start
				return (
						<View style={styles.container}>
	
						<Text style={styles.welcome}>
						Welcome to React Native!
						</Text>
						<Text style={styles.instructions}>
						To get started, edit index.android.js hehe
						</Text>
						<AdUnit pubId="ca-app-pub-3940256099942544/6300978111"></AdUnit>
						<Text style={styles.instructions}>
						Shake or press menu button for dev meno
						</Text>
						<AdUnit pubId="ca-app-pub-3940256099942544/6300978111"></AdUnit>

						</View>
				);
		},

});

var styles = StyleSheet.create({
  container: {
			flex: 1,
    justifyContent: 'center',
    alignItems: 'center',
    backgroundColor: '#F5FCFF',
  },
  welcome: {
    fontSize: 20,
    textAlign: 'center',
    margin: 10,
  },
  instructions: {
    textAlign: 'center',
    color: '#333333',
    marginBottom: 5,
  },
});

AppRegistry.registerComponent('admobe', () => admobe);

MainActivity.java

package com.admobe;

import android.app.Activity;
import android.os.Bundle;
import android.view.KeyEvent;

import com.facebook.react.LifecycleState;
import com.facebook.react.ReactInstanceManager;
import com.facebook.react.ReactRootView;
import com.facebook.react.modules.core.DefaultHardwareBackBtnHandler;
import com.facebook.react.shell.MainReactPackage;
import com.facebook.soloader.SoLoader;

public class MainActivity extends Activity implements DefaultHardwareBackBtnHandler {

    private ReactInstanceManager mReactInstanceManager;
    private ReactRootView mReactRootView;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        mReactRootView = new ReactRootView(this);

        mReactInstanceManager = ReactInstanceManager.builder()
                .setApplication(getApplication())
                .setBundleAssetName("index.android.bundle")
                .setJSMainModuleName("index.android")
                .addPackage(new MainReactPackage())
                .addPackage(new ReactAdMobPackage())
                .setUseDeveloperSupport(BuildConfig.DEBUG)
                .setInitialLifecycleState(LifecycleState.RESUMED)
                .build();

        mReactRootView.startReactApplication(mReactInstanceManager, "admobe", null);

        setContentView(mReactRootView);
    }

    @Override
    public boolean onKeyUp(int keyCode, KeyEvent event) {
        if (keyCode == KeyEvent.KEYCODE_MENU && mReactInstanceManager != null) {
            mReactInstanceManager.showDevOptionsDialog();
            return true;
        }
        return super.onKeyUp(keyCode, event);
    }

    @Override
    public void onBackPressed() {
      if (mReactInstanceManager != null) {
        mReactInstanceManager.onBackPressed();
      } else {
        super.onBackPressed();
      }
    }

    @Override
    public void invokeDefaultOnBackPressed() {
      super.onBackPressed();
    }

    @Override
    protected void onPause() {
        super.onPause();


        if (mReactInstanceManager != null) {
            mReactInstanceManager.onPause();
        }
    }

    @Override
    protected void onResume() {
        super.onResume();

        if (mReactInstanceManager != null) {
            mReactInstanceManager.onResume(this, this);
        }
    }
}

ReactAdmobManager.java

package com.admobe;

import android.util.Log;

import com.facebook.react.uimanager.ReactProp;
import com.facebook.react.uimanager.SimpleViewManager;
import com.facebook.react.uimanager.ThemedReactContext;

import com.google.android.gms.ads.AdListener;
import com.google.android.gms.ads.AdRequest;
import com.google.android.gms.ads.AdSize;
import com.google.android.gms.ads.AdView;


public class ReactAdmobManager extends
        SimpleViewManager<AdView> {
    private String mAdUnitId;
    public static final String REACT_CLASS = "RCTAdmobView";
    private ThemedReactContext mReactContext;

    /** prop to set pubId and load the Ad */
    @ReactProp(name="pubId")
    public void setPubId(AdView view, String pubId) {
        Log.d(REACT_CLASS, "Setting Pub Id to " + pubId);
        this.mAdUnitId = pubId;
        loadAd(view);
    }

    /** dummy prop */
    @ReactProp(name = "loadAd", defaultBoolean = true)
    public void setLoadAd(AdView view, Boolean load) {
        Log.d(REACT_CLASS, "inside set src");
        if (load == true && mReactContext != null) {
            Log.d(REACT_CLASS, "loaded ad");
        }

    }

    @Override
    public String getName() {
        return REACT_CLASS;
    }

    @Override
    protected AdView createViewInstance(final ThemedReactContext reactContext) {
        Log.d(REACT_CLASS, "inside create view");
        this.mReactContext = reactContext;
        Log.d(REACT_CLASS, "the ad unit ID is: " + mAdUnitId);
        final AdView adView = new AdView(this.mReactContext);

        loadAd(adView);
        return adView;

    }

    void loadAd(final AdView adView) {
        Log.d(REACT_CLASS, "Sending Add with PubId: " + mAdUnitId);
        if (adView.getAdSize() == null) {
            adView.setAdSize(AdSize.BANNER);
        }
        if (adView.getAdUnitId() == null && mAdUnitId != null) {
            adView.setAdUnitId(this.mAdUnitId);
        }
        AdRequest adRequest = new AdRequest.Builder()
                .addTestDevice("YOURTESTDEVICENUMBER")
                .build();
        adView.setAdListener(new AdListener() {
            @Override
            public void onAdLoaded() {
                super.onAdLoaded();
                Log.d(REACT_CLASS, "onAdloaded");
                int width = AdSize.BANNER.getWidthInPixels(mReactContext);
                int height = AdSize.BANNER.getHeightInPixels(mReactContext);
                adView.measure(width, height);
                adView.layout(0, 0, width, height);
            }

            @Override
            public void onAdFailedToLoad(int errorCode) {
                super.onAdFailedToLoad(errorCode);
                Log.d(REACT_CLASS, "failed" + errorCode);
            }
        });
        if (this.mAdUnitId != null) {
            adView.loadAd(adRequest);
        }
    }

}

ReactAdMobPackage.java

package com.admobe;

import com.facebook.react.ReactPackage;
import com.facebook.react.bridge.JavaScriptModule;
import com.facebook.react.bridge.NativeModule;
import com.facebook.react.bridge.ReactApplicationContext;
import com.facebook.react.uimanager.ViewManager;

import java.util.Arrays;
import java.util.Collections;
import java.util.List;

public class ReactAdMobPackage
implements ReactPackage {
    @Override
    public List<NativeModule> createNativeModules(ReactApplicationContext reactContext) {
        return Collections.emptyList();
    }

    @Override
    public List<Class<? extends JavaScriptModule>> createJSModules() {
        return Collections.emptyList();
    }

    @Override
    public List<ViewManager> createViewManagers(ReactApplicationContext reactContext) {
        return Arrays.<ViewManager>asList(new ReactAdmobManager());
    }
}