You should definitely reapply! I am about to enter into my 2nd year of PhD at a university I was previously rejected from. Although when I first applied I had experience of my field outside my degree, it wasn't enough to get me the place. And I had applied and was interviewed for several other projects around the same time, so I was juggling too many balls. After graduation I managed to get even more experience and 6 months later I applied again and got it. I think once you've graduated you have a better idea of what you want from a project and where your interests lie, and I think that comes across in the interview. Don't worry about prejudice, you will simply have to tick a box on the form saying you've applied previously in 200x and they'll see that with additional experience you are now even more determined to undertake the project. Good luck!