bids?

No one will hold it against you that you're in the honors college. Most houses will think that's awesome. About 800-900 girls rush and the numbers keep increasing every year. Usually about 600 girls get bids because there are 10 houses and the average pledge class size is about 60 girls. That means 200 girls don't get bids but the majority of those are girls who drop out for various reasons. If you keep an open mind throughout the process and are nice/polite to everyone at every house you will get a bid somewhere. It may not be your top choice since rush is getting more and more competitive each year, but you will get a bid somewhere.

Yes, if you maximize your options it is very likely you will receive a bid. Like the above poster said, most girls who go bidless drop for their own reasons and those who do get cut are often sophomores\ juniors or girls with very low gpas. You can find women in the honors college in just about every chapter and most chapters will see it as a sign that you take your academics seriously. And yes, pledge class sizes are determined by the number of women rushing but hopefully upcoming colonizations will help bring those numbers down a little bit.

The president of my chapter is in the honors college so yes every single house will see that as a good thing. Definitely maximize your options, a lot of girls who get cut or drop are the ones who don't try at the houses they don't like and only are nice to the one(s) they want. Risky move especially because the house I'm in which i LOVE was a house I didn't immediately like.