Several Rider writing majors have gone on to creative writing MFA (Master's of Fine Arts) programs. The resources here will help give you an overview of what MFA programs look like, how to apply, and what you can do with the degree.
There are also programs that offer an M.A. in creative writing, but generally speaking the MFA is the preferred degree. While the MFA used to be a terminal degree (meaning the highest degree you can get in a specific field), over the past few years more universities have begun to offer PhD programs in creative writing, which makes it more difficult to secure a tenure-track job as a creative writing professor with only an MFA. Even with a PhD in creative writing, it will be difficult to find a tenure-track job unless you have strong publications (several pieces in literary journals, or preferably a book), and are willing to move wherever the job may be. To give you an idea of the odds you'll be facing, the AWP has found that in 2009-2010, U.S. universities posted only 78 tenure-track faculty positions in Creative Writing, but 220 programs offered the MFA or PhD in Creative Writing.
That said, when I was an undergraduate my professors told me that the jobs were few and the stakes were high, and I still went to grad school and ultimately got a tenure-track job as a creative writing professor. So there's no reason you can't do the same. My advice is to find a program that will offer you funding (via a T.A. position or fellowship) so that you don't put yourself into debt, and if nothing else you've spent a few years focusing on your writing, learning from other writers, and furthering your education. If you get accepted without funding, it's a tougher decision.
Start early! It takes a lot of research to find the right schools, put together your application materials, etc. You'll want to research each program's faculty and the kind of wiritng they're publishing. Find faculty members who are doing the kind of work you want to do! Some programs will be a good fit, and others won't. It often takes more than one year of applying before you're accepted. In the meantime, keep working on your writing, as your writing sample is the most important part of the application!
The AWP Guide to Writing Programs is a smart place to begin your research.