With the old terminal, once you arrived at the transit terminal, they have the line at the left for those with short time frames for connections, so unless overly congested, you should get through security within 0-10 minutes. The gates do close 20 minutes before (and sometimes even a little earlier), so do be at the gate early, even though all you will do is scan your boarding card and go down the stairs to the cramped area and wait for the bus.

For the new terminal, with the jet bridges, you should be fine.