B’h I hold of the other Torah where drinking beer is not usser. In addition, if it is a glass cup and clean there is no issue of traifos since glass can not be mikabul tumah.
The only issue with a bar is drinking with goyim and unless this girl is not Jewish there is no Halacha issue of him drinking.
Now, should a boy drink on the second date? Who are we to answer what is appropriate or not? If this girl is the type not to mind, then there is nothing wrong. The fact that she is asking this question, means it bothers her and therefore she should not date him because obviously, he feels it is appropriate.
Or maybe it was a bad date and he needed alcohol:):) Who are we to judge?