Flutter update BottomNavigationBar

I think it is way more elegant to use PageView instead of TabBarView specially in your case.

class BottomBarExample extends StatefulWidget {
  @override
  _BottomBarExampleState createState() => new _BottomBarExampleState();
}

class _BottomBarExampleState extends State<BottomBarExample> {
  int _page = 0;
  PageController _c;
  @override
  void initState(){
    _c =  new PageController(
      initialPage: _page,
    );
    super.initState();
  }
  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      bottomNavigationBar: new BottomNavigationBar(
        currentIndex: _page,
        onTap: (index){
          this._c.animateToPage(index,duration: const Duration(milliseconds: 500),curve: Curves.easeInOut);
        },
        items: <BottomNavigationBarItem>[
        new BottomNavigationBarItem(icon: new Icon(Icons.supervised_user_circle), title: new Text("Users")),
        new BottomNavigationBarItem(icon: new Icon(Icons.notifications), title: new Text("Alerts")),
        new BottomNavigationBarItem(icon: new Icon(Icons.email), title: new Text("Inbox")),

      ],

      ),
      body: new PageView(
        controller: _c,
        onPageChanged: (newPage){
          setState((){
            this._page=newPage;
          });
        },
        children: <Widget>[
          new Center(
            child: new Column(
              mainAxisAlignment: MainAxisAlignment.center,
              children: <Widget>[
                new Icon(Icons.supervised_user_circle),
                new Text("Users")
              ],
            ),
          ),
          new Center(
            child: new Column(
              mainAxisAlignment: MainAxisAlignment.center,
              children: <Widget>[
                new Icon(Icons.notifications),
                new Text("Alerts")
              ],
            ),
          ),
          new Center(
            child: new Column(
              mainAxisAlignment: MainAxisAlignment.center,
              children: <Widget>[
                new Icon(Icons.mail),
                new Text("Inbox")
              ],
            ),
          ),
        ],
      ),
    );
  }
}