I have the experience you need on App development for this Project. User experience and interactive UI design, as well as html5 based on JavaScript, jQuery and mobile frameworks like jquery mobile or Kendo UI.
I propose to make your App under an html5 hybrid approach to make the code highly maintainable and to give you more plaforms than just the Android and iOS you are asking for, I would use as well an Apache Cordova approach for this. To make calls back and forth between the App and twitter api, jsonp calls should suffice.
Time proposed is just a placeholder, since you have not described your Project and it could´pretty easy and fast to develop, or a big one... so there is no data to uphold a calendar and plan for the development.
Please, feel free to ask any further questions. I will be very glad to help you on this Project.