Will I be able to get into the University of Washington for grad school?

Okay I have my A.A. degree from a Florida Community College and will be attending the University of South Florida in the fall. I am majoring in Social Work and I am curious if all goes as planned and I get my BSW if I would be able to get my MSW from the University of Washington? I am originally from Washington state and the family is really pushing for me to go back home, they hate that I am so far away just for school. So would UW be an option for me? If not please make ANY recommendations for Grad schools either in Florida our out of state. Thanks! Best Answer gets 10 pts!