It shouldn't be a problem. It's likely that you're not the only transfer student rushing. Generally, bid day activities include receiving your bid and spending some time with your new sisters... icebreakers, games, food, gifts for the new members, and maybe a pledging ceremony.
Talk to your rho chi. If you do receive a bid, she will contact you privately to let you know which sorority it's from, and she'll give the sorority a heads-up that you won't be able to attend all the bid day activities. Then, you can meet up with everyone once orientation is over, or just sneak out of orientation early if you want. You will have plenty of time to get to know your new sisters later on.
Good luck!
