From what I hear, the ST IV bridge for the Ent-A was never intended for full-time use, it was just something they literally threw together at the last minute just for filming that one scene. Who knows, that may have been true in-universe as well!
That's exactly what happened -- the
Enterprise-A bridge in
Star Trek IV was a redress of the
TMP onward bridge set, painted white. What we saw on screen was literally the one angle from which it could be shot. There's a picture of it that shows the point where it becomes "unfinished" with the older beige color scheme.
Actually they painted pretty much the entire bridge set white, added those silver bulkhead supports, the baseboard lighting panels, and altered most of the main consoles with the first ever Okudagrams.
You can see this best in the footage included in Entertainment Tonight's Trek 20th anniversary special.
http://www.youtube.com/watch?v=uDy-7vOkKVw
You can see most of the set in this clip during the intro with the host. During James's Doohan's interview he's sitting at the science station which has Okudagrams on both of it's roll out consoles which were never seen in the film. When they get to Nichelle Nichols' interview, she's sitting at the engineering station (to the right of the communications console) which still has the old TMP style flashing lights and graphics. During Walter Koenig's interviews you can see the console behind him has also been altered. So they probably only made new graphics for that back half of the bridge.
In this clip from GMA (also from 1986) at 5:18 you see a reverse shot of Joan Lunden interviewing the cast and you can clearly see that the console to the right of the main viewer has been painted white, has a silver bulkhead support but doesn't have any Okudagrams.
http://www.youtube.com/watch?v=rgtjG66nbno
Judging by the fact that they redressed most of the set all the way around, they were either doing it to make sure Nimoy could get any coverage he wanted for that last scene of TVH or just doing as they much as they can in anticipation of the new film.
In a 1987 Starlog interview about the then in production TNG, David Gerrold wrote that they had converted most of the bridge set to the battle bridge but that the rest of the set was being kept safely, ready for Trek V. For the pilot of TNG, they pretty much stripped and struck the entire bridge set except the two turbolift alcoves and the standing console between them. This clip also from ET shows the bear bones set after most of it had been taken down.
http://www.youtube.com/watch?v=Bi3X_6eEJBM
According to one of the commentaries on one of the dvds, the same set was supposed to be used for Trek V, but the walls and consoles that were saved (after they converted it into the battle bridge for TNG) were left outside and during a severe rainstorm the tarps covering them came undone. The wood framing warped and the set pieces no longer fit together causing the crew and production designer Herman Zimmerman to come up with a new design last minute for Trek V. The only things left from the original were the two door alcoves, the helm console, the railings and the platforms.
As much as I like both the Trek V bridge and the altered version for TUC, the one thing I wish they re-build was that great jet engine-like ceiling designed by Mike Minor. Interesting to note that those two turbolift alcoves survived all the way up to Nemesis when they were part of the Enterprise-E bridge.