If you are worried that you will cave in at the bar then I would tell her before you go. If she doesn't like that you don't drink and that you even don't want to be in a bar then she is not the right girl for you.
Can you imagine trying to a have relationship with someone who wants to go out and party and you don't? Tell her you are trying not to drink because you drink more than you think you should and ask if she would like to get ice cream or something like this after dinner. If she says no, no time wasted for either person.