WE=work experience
I was also an international student (did my BA then worked for a little over a year in the US) and I understand your doubts and concerns. But don't attend a school that won't offer you opportunities in the future just so you can stay back. You have solid GRE and grades and with work experience you could do a lot better. Besides, if you're really serious about an MPP you will probably need some WE to get into good grad schools.
Evaluate your priorities. If your priority is to continue your stay in the country and think about the next step after you're done with the Bush School and then go ahead and do that. But sooner or later, lack of work experiences will be an issue for employment . On the other hand, if you can get some solid experience in your home country (or another country, even if it is NGO work) go head and explore your options. An MPP program should complement your career choices so take some time to formulate that choice.
If you get into Bush and decide to attend it, explore the possibility of taking a year off before enrolling (if they offer that option). That way you are guaranteed to come back with a better understanding of your goals. Good luck!