One fairly simple explanation actually explains another mystery, too.
Remember that turbolifts do not move on cables or rails like today's lifts. They are capable of overtaking, just like taxi cabs today. This means that a lift cab held in readiness near the bridge does not block other lift cabs from accessing the bridge. Not if there's a "parking lot" in the turboshaft at or near bridge level.
Now note that the turbolift station in TOS is not at the back of the bridge, opposite the viewscreen and behind Kirk's back. It's a bit off to the side. In TOS movies, there are multiple lifts, and they change location at each refit, without affecting the exterior looks of the ship at all.
Now, it could well be assumed that there is a central turboshaft in Kirk's ship, right at ship centerline, climbing all the way to the bridge. And then there's a little side branch that ends at the door... Perfect for the "taxi rank" system where multiple cabs are waiting, and one pulls to the doors whenever somebody needs a ride down while another remains waiting.
In the movies, there are probably two side-by-side vertical shafts, just as seen at the Recreation Deck (a facility that would have to be located at ship centerline, close to saucer axis, because there's no room for it elsewhere). And then these convenient side branches to serve the two turbolift stations at the bridge, the length of the branches being easily modifiable.
In both cases, we would have to assume that the bridge is not quite flush with the top of the ship, but lies a bit lower down, in order for the side branches to exist. But we have to assume that in any case in the movies, because the sets from the later movies really wouldn't fit inside otherwise. And it makes good sense in ST:TMP as well: we notice that when Spock boards the ship through a docking port at the very top of the ship, he then needs to enter a turbolift in order to access the bridge, suggesting the two are at different heights.