Is it rude to ask wedding guests to byo alcohol? Please help!!?

Yes, it is rude, and no, there is no "good" way to word this on the invites. You as the hosts are responsible for providing refreshments for your guests. If you ask guests to help you foot the bill for your party, they are no longer your guests. Don't provide anything you can't afford. There is absolutely nothing wrong with an alcohol-free wedding (or a wedding with just champagne for toasting).