Disclaimer: I am not a language teacher, but I've done a lot of language study, and a close relative is a language teacher.
Fluency varies. You will, in all likelihood, never sign like a native (I say "in all likelihood" just to cover my ass - very, very, very rarely, an adult can learn to be native in a language). So what you're really asking, then, is "how long before I'm competent enough in the language that I feel comfortable in most situations?"
There was a linguistics professor at UIUC in the 70s named ... I think Sandra Savignon. She coined the term "communicative competence". The idea behind communicative competence is that there are different situations where you are more or less fluent. So, right now, you may be able to express yourself very well on a given topic of conversation; in that area, with certain limitations, you have communicative competence. "Fluency" is just expanding the areas within with you are competent.
It's impossible to guess at a timeframe. That varies on how easily a person learns languages; how well they learn the specific language in question; how much they're able to interact with native users of the language at an early stage in the game; and other factors. But the best thing you can do to increase your fluency is to interact with native speakers as much as possible, even if your use of the language is imperfect.
