How likely am I to get a bid?

If you stick with the process the chances are very good that you will get a bid. But stay open to any and all that you get invited back to regardless of whether they were your top choices or not. Cuts are very heavy the first two rounds especially for some chapters. It's just a numbers game. Making it through the first is good but don't be disappointed if you don't get all of your top 4. It is ok to have a favorite but don't set your mind and heart on only that one. When people do that, they tend to not get the most out of the experience and can even set themselves up for disappointment. You will end up where you are meant to be!

There is really no way to know your odds because there are literally a thousand factors that play into it. Like someone else said, if you maximize your chances by returning to the maximum number of houses that ask you back you will most likely get a bid. Most people who follow through to the end get a bid. There might be occasional exceptions but ususally there is something else at play like questionable grades. it's not like super competetive SEC schools where there might be hundreds of people left without one. Now whether or not your first choice from the start is where you end up is hard to know and it's definitely possible but statistically not as likely. Just be yourself and keep a good attitude and you will be fine!