First commercial production of Benedictine was in the 1870s, so the bottle won't be older than that. Benedictine bottles are difficult to date without the label, but there are some useful pointers here:
Note that the usual indicators for age from bottle production methods used in America don't apply here. This will almost certainly be a European-produced bottle (probably French) where traditional glass-production methods were used into much later times. At a guess I would say this one is from the early 1900s.