Why? Parker is funny yet incredibly smart and noble. Peter also makes friends with anyone, even people as visceral as Kaine and Wolverine.
That's because they've known Peter for a while compared to Psylocke, who just barely met him. Kaine knows Peter, because he's a clone, and Logan knows Peter, because he's one of the few people that Logan trusts, and they went through a lot together.
So there ya go, knowing somebody for a while and eventually getting to see there true value makes all the difference, I don't see why Betsy would immediately dislike Peter from the get go considering she's good with nightcrawler and iceman, she'd eventually see Peter for all the ultimate heroism he has done for all the day and would be able to make pals or even something more.