...the one that destiny lead to her...
In the begining, when they first met, it seems that it's a simple fact, that Watanuki has a wish and Yuuko would grant it when he worked enough at her shop to pay it. It really seems that at the begining he is simply her personal slave, with all the stuff she makes him do, but later on during the series, we actualy see the changes, and the fact how deep the bond becomes, and how she was actually waiting for him to arrive at her shop.
The encounter in the first volume actually is not their first encounter. Their relationship goes much deeper, because Yuuko was there when Watanuki was created, when Shaoran stopped time and Watanuki was born from the tabu magic. We could almost say she was his god mother.
During the series, we actualy see that she cares a lot about the boy even if she never lets him see, well, maybe towards the moment when she knows her end is coming.
We can also say that Watanuki is her pupil, he has enough power to take over her shop when she will be gone, or maybe not, but still during the whole series she is the one who helps him grow, and she is the one who is has the burden of not being able to tell him the truth about himself, he has to find out alone - and also lets him do things alone so he can grow and mature, she helps but at the same time she only observes.
In the end, we know as a fact that Yuuko and Watanuki care for each other deeply. The moment Yuuko begins to disappear, we can see how desperate Watanuki is and wants her to stay, and she tries to tell him that it was meant to be that way, but that she cares really deeply for him, and that she is happy that she was able to meet him.
I think their bond is special, not because of what happens but also because both should not exist, Yuuko's time was stopped by Clow and she was stuck in a moment of her life, while Watanuki because of a similar thing was born... in the end we all know that he actualy is part of Shaoran, who also stopped time to save Sakura, and Watanuki was born from him. It's something powerful that makes their bond really strong.