Can you check with one of your coworkers and see if one of them is able to cover your shift? Perhaps you can offer a trade -- "I'll take your Friday night shift if you can cover this one shift for me." My experience is that most managers of retail, restaurant, and similar jobs are amenable to switches as long as all shifts are covered.
Okay...just to finish up my [unpopular, but whatever] statement here...
Be aware that some [maybe all, I'm not sure] chapters will have requirements about who they can bid. For example, some chapters may say that they are not allowed to bid a girl who only attended one party, or only attended two parties. This is why I say it will hurt you - if you can only attend one party, there will probably be groups who are required to cut you due to National guidelines. This may also apply to two parties for other groups.
Whether or not this will hurt you depends on the chapter.
There are some who may decide not to bid someone who missed an event. Then there are some who will just go ahead and invite you back again. It just depends.
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"Remember that apathy has no place in our Sorority." - Kelly Jo Karnes, Pi
if there isn't a way for you to get out of it (switching shifts?) let them know the day before. be super apologetic (i.e. "i just want to let you know ahead of time that i have to work tomorrow during the second round of open houses. i apologize and truly wish i could be here instead.") do you have recruitment counselors? if you do, i'd get a note from your manager saying you were scheduled to work and there wasn't a way to get out of it. then the counselor would give a copy of that note to the chapter. it's the same as if you had class...would they expect you to skip class for a recruitment event? probably not.