How long does it take to be accepted into a service mission? (26+)

I don't currently live in my country, but I joined the church here. I'm now planning to leave within about eight months.

But I'd like to help the church here more actively while I’m in the area. My current calling is ward missionary, but I've never actually been asked to do anything special. I've been thinking about the possibility of a 26+ service mission, which, from what I've read, doesn't require the endowment (I can do it this winter) and is flexible.

But how long does it take for the application to be accepted, if I were to ask the bishop?