Is this a good New School Club Idea - Student Senate?

That's a great idea! And an awesome way to book your transcript for college. You can add that you founded a group that dealt with social issues, government and politics. The bill writing part helps students work on writing skills and thought process. (try to get an English teacher involved) Presenting/debating the bill we help you all work on your interpersonal skills and speaking skills. - All of which look good to colleges. Plus it sounds really fun too! You can even get local politicians come in once and a while. Good luck!