If you are worried about her safety you can always ask her to send you a text/give you a call at a designated time to let you know that all is well. It's easy enough to excuse yourself from the table for a minute to make that kind of call. It sounds to me that she wanted you there as a security blanket. Ask her if she feels safe at other times when she is out without you. There really isn't any reason if she is out in a public place and not consuming a lot of alcohol for her not to feel safe on a first date.
Make plans of your own next time she's out. Go and do something that you enjoy that isn't her favourite thing to do. Or for that matter stay home and do something that she doesn't like to do. I love my alone time. I get to watch my cooking competition shows that my husband isn't terribly fond of. I also get to make myself refried bean burritos and have ice cream with butterscotch sauce for dessert. I look forward to my dates with myself quite a lot.
Everything will be ok in the end. If it's not ok it's not the end.