In terms of etiquette, the more formal the invitation, the more rude it is to bring uninvited guests.
But as Roland Deschain would say, "the world has moved on." Expecting anyone to hold to any sort of predetermined and agreed upon rules of etiquette has become more limiting than comforting these days – in large part because we are both exposed, and have access to, a much larger social world/community. Which is a Very Good Thing™.
In that light, it is not accepted as generally rude to bring a friend along to when invited somewhere for something like coffee/drinks – unless it's clear that it's a one on one date. If you're unwilling to go the extra mile to make it clear you want to see her alone, then you must not only suffer the consequences, but would be a fool not to use the chance to gain an additional ally – her friend – in your romantic quest.
Being the kind of guy who welcomes surprises, copes with unexpected change, and is generally inviting and inclusive are incredibly desirable traits, and having her friend's corroboration that it's not just "in her head" is truly valuable. On the flip side, if you instantly "deflate", get more distant/distracted, or even cool to her friend, you're digging your own grave.
Long story short: rules be damned, seize every opportunity not only to impress your person of interest, but also his or her friends and family. Oh yeah, and be frickin' patient. Intention and expectation are two very different things! When you finally do have some "alone time" later on, the results should speak for themselves. 🙂
Is it rude to bring a previously unmentioned third person to coffee/drinks with a member of the opposite sex?