Actually I don't even know why shipping had to be a factor in this. And if I remember correctly, Bianca had lost, so she shouldn't have even been there to begin with anymore just like Ash left when he lost.
The writers write how he wants. He didn't make Trip stay. But Bianca was there to cheer on Ash. Why do you have a problem with that?
Bianca was more of a friendly rival than a real rival to Ash, so of course she's there to cheer on Ash.