Quick update, Capitol Bells now includes the Senate. The big update is currently under review by Apple's app store, and it should be freely available for download any day now. If you can't wait, you can check out a demo here on app.io - the real version looks better than this though.
The Senate side of Capitol Bells has all the same functionality as the existing House side app. One important difference between the two versions for you floor wonks out there is that this version does natively scrape for current bills under consideration. Instead, it uses the Sunlight Foundation's API for "Upcoming Bills," which they scrape for updates every fifteen minutes.
If you would rather follow the Senate than the House, you can open up the setting menu from either side of the app and choose you "default."
I hope Capitol Bells is as popular in the Senate as it is in the House!