In every other area of life, the person who waits is never the first to speak. Think of placing a telephone call: when the other person picks up, he says hello first, not you. When you reach the head of the line, it is the clerk who starts with “how may I help you”. In my opinion the confessional ought to be exactly the same - it is the priest who should speak first. Logically you don’t know if the priest is even ready until he gives you some signal.
In my opinion the way the ritual is written is a bit awkward; but if you think about it this way: that the act of getting into the confessional is the equivalent of saying “Bless me Father I have sinned”, the equivalent of a telephone ringing, then logically the priest should follow suit and bless you.
Remember the ritual is written for confessions done in a confessional but also for those done face-to face, where you can tell by body language that he is ready and then you can begin with “Bless me Father”. But then again, if he is going to bless you, then when? While you are speaking? That’s awkward.
Besides, most confessional boxes have cells on both sides of the priest; you wouldn’t want to be saying “Bless me Fath - Father? Are you there? Oops sorry” while he is dealing with the other penitent.