I always liked the idea of there being one in that gangway around the TOS bridge though. It's a clever idea.
Me too. I also like how it actually gives the additional door on the bridge in TAS some purpose: it doesn't simply lead to a secondary turbolift, but instead leads to the gangway around the bridge that happens to contain various additional things (including the toilet). It's a logical addition, albeit one we never saw confirmed on-screen.
Alas, in TOS that door is missing, so we are left to theorize how they might access the gangway in the live-action Star Trek...
One other idea is that there are doors on the bridge which lead to the outer gangway, but which don't look overtly like doors, instead resembling wall panels. On some commercial airliners the areas in which the cabin crew sleep during long haul flights are in a door which is designed to look like a wall panel, which slides aside to allow access. It's less practical than TAS's secondary door, but is probably more asthetically pleasing in terms of the bridges contours.