Rose had plenty of friends on the Powell Estate and every one of them would have her number. But they would all still be grieving for her and her mum. They all thought she was dead, so just imagine their reaction if The Doctor goes up to one of them and asks for Rose's mobile number. Picture this:
" Excuse me, yes could you please give me the number for your dead friend Rose Tyler, I thought I may be able to reach her even though she's dead and buried"
Or I suppose he could pretend to be in denial, and refuse to believe she was dead, that wouldn't be too hard seeing as he knew she wasn't actually dead. That could work considering most of her friends thought he was a crazy mad man anyway. But if that didn't work then he would just have to tell the truth, so which one of her friends would understand the most if he told them everything? Shireen? Keisha?
From what Rose had said about Shireen she was quite a loud mouth, if he told her then she might go off and speak to the police or something or she could speak to everyone else and tell them that he was a loony and no one should speak to him, then he would never get her number, but she was one of Rose's best friends so surely she would jump at the chance to call her and speak to her too even if she could never see her again. That's all he wanted, just to hear her voice tell her he was sorry, tell her he loved her, make sure she was okay.
Then there was Keisha she lived just round the corner and she probably would understand the most seeing as she had been rapped up in one of their adventures with her brother Jay (book The Feast of the Drowned) but then again nearly everyone in London had encountered aliens, The Sycorax on Christmas day and the Slitheen in Downing street. His mind was made up and he decide that his best chance of getting Rose's number was to go and pay Keisha a visit.