Interesting... What in ST3 would suggest the use of impulse power for the trip? Obviously the ship was warp-capable, as evidenced by the later time warp.
Is it just because the ship might have been out of warp when receiving the news of Earth's plight that you deduce she wouldn't have gone to warp at any point? Starships commonly drop down to impulse long before reaching Earth. And Kirk was in no hurry to arrive...
The Movie era FX were remarkably consistent with depictions of impulse and warp drive. In fact, nearly every time we do see the BOP at warp it is shown streaking through space with a yellow tail behind it, so we can know for sure when it is and isn't at warp.
What actually got me was the fact that the Bird of Prey's launch is depicted as being very near to the time the probe entered Earth orbit. The very next scene after this, we have Sulu reporting "Estimating Planet Earth, one point six hours present speed." If the Bird of Prey is going at half the speed of light at this time, that would put the ship well inside the orbit of Jupiter. Which is, I think, a LITTLE late to start wondering where your escort is.
In either case, it's the same issue as in STXI, where it appears the entire voyage is edited out except for the last leg of the trip just before their arrival. The question here involves the editing of the scene: did the probe arrive over Earth at the same time the Bird of Prey took off, or did the probe arrive over Earth only a little before Kirk would have? In the former case, it would mean the President watched the Probe rip Earth a new asshole for a couple of days before he decided to put out that planetary distress signal. In the latter case, it means that Starfleet sat there and watched the probe speeding towards Earth and didn't put out a warning to any other Federation members--Vulcan included--or give any other indication that Kirk and crew would have intercepted during the two to three day trip to Vulcan (and he WOULD have picked it up, since Chekov had programmed the onboard computer to interface with the Federation memory bank).
The only solution that works here is that the scenes worked out the way they were depicted: the probe really DID arrive quickly and with little warning, entering Earth orbit just as Kirk was leaving Vulcan. This means that the Earth-Vulcan run only takes a couple of hours at impulse and a matter of
minutes at warp.
And not that things aren't complicated enough, but I might as well invoke the now infamous "Four days there, four days back" to the Klingon Homeworld in Enterprise. The pattern is that warp drive is--under certain circumstances--alot faster than we've been lead to believe, so much so that five to ten minutes between Earth and Vulcan may not be that much of a stretch after all.