I've personally been accepted into two accelerators.

The wait time depends on the accelerator. For one accelerator, I didn't hear back until at the absolute last minute (the week before it started). For another accelerator I heard back about a month before it started.

In terms of improving your chances for an accelerator, having an alumni give you a reference is a big help. Also continuing to show signs of traction and growth is a big help as well. There are a handful of other ways to get the attention of the decision makers at the accelerators too.

Call me if you need help getting into an accelerator.