Hi there, it's nice to see a UK member! I'm from Newcastle so not far from you, welcome to YT.
Where did you get your Yorkie from? was it a rescue or were her old family just looking to re-home her? Have you asked if she has had problems with biting in the past? She is probably just nervous as you have only had her for 3 days and everything is very new to her. Give her time, approach her slowly and let her sniff your hands before you go in to stroke her so that she feels calmer about the situation. Is she play biting or is it more of a nervous bite?