According to the developers blog, "The Beta will be geographically rolled out, with three different regions planned; US-West, US-East and Europe turned up at slightly different times. Tentatively we are aiming to turn up the first Closed Beta during the week of February 28." The blog also mentions that applications for the beta have exceeded well over a hundred thousand, so expect typical chances coming out the door for beta invites.
K2 is supposedly changing a lot from the original game, while trying to keep the general feel the same. They have made extremely long blog posts in the past few weeks detailing a lot of the specific changes and tweaks that they are doing to make the game a much more enjoyable experience, despite moving over to a free-to-play cash shop styled game. I rather enjoyed All Points Bulletin despite its many flaws, so I am hoping that K2's tweaking and prodding does the game good, and that a second flop doesn't end up occuring. Expect an open beta release of APB: Reloaded sometime near the middle to end of the year, with the full game releasing soon after. So far K2 has been vague on a release window, but they've said that many of the beta phases should be adjacent to release, so it shouldn't be long now.