Can I apply to graduate school twice?
If I interpreted your question correctly, you're asking if you can apply for graduate school one year, and, if rejected, re-apply the following year. Unless there are some field-specific norms that I am unaware of, the answer is almost definitely yes. Of course, for you to stand a chance of not being rejected a second time, your application should be significantly improved. In your case, that seems likely, as you'll have had an extra year of schooling, possibly stronger references, perhaps some research experience. Good luck in any case!