She asked me out yesterday but I turned her down.I feel bad,What should I do (Girls please help)?

Yes, definitely apologize. Not for saying no, but for hurting her. Explain to her that the reason why you're saying no is not because she's not good enough for you but because you're (from what I can see) still not fully healed from the pain of losing your girlfriend. Also tell her how special she is to you and how grateful you are for her friendship, but explain that it will probably remain that way -- as a friendship. I'm sorry about your girlfriend, but always remember that she's now in a better place :)