I don’t remember at what point in the movie he showed up at the conference, but there’s at least a day, at minimum, of C3PO and R2D2 wandering around before getting captured by the jawas, an unknown amount of time riding the sandcrawler, and from there, at least two days before getting to Mos Eisley. So, with hyperdrive, plenty of time for him to get to the meeting. Doesn’t seem like any complex contortion needed to explain it away. Heck, a couple hours might be enough.
That wasn't the point, the original question was whether he traveled in his star destroyer, or took a shuttle service.
But remember details such as: Luke and Obi-Wan have their "we have to get to Alderan" moment in Obi Wan's house, right before they cut to Tarkin ordering the Death Star to travel to Alderan. So Leia and Vader were already on the Death Star well before the heroes went to Mos Eisley.
EDIT:
I went and checked it out, there is an actual shot of a Star Destroyer approaching the Death Star, just after Obi Wan gives Luke the light saber. After that, Vader is on the Death Star. So I was correct, Vader
did in fact travel to the Death Star in his Star Destroyer which was shown at the start of the movie, just to clear up that particular debate.
So a rough time line is that Vader captures Leia, can't find the plans, orders a ground troop detachment, then we see a shot of Vader's Star Destroyer moving away from the planet. The next time we see it, it's approaching the Death Star. So what this suggests is that Vader
immediately left for the Death Star after ordering a ground troop detatchment to secure the contents of the escape pod. But remember, at that point in time, Vader only said the plans are
in the pod. e.g. they had no reason to have a blockade, yet.
But hey, two nights are shown to pass between Vader leaving orbit around Tatooine and getting to the Death Star. And one night is shown passing between him ordering the pod retrieval and the troops finding droid parts. if additional Star Destroyers were ordered to Tatooine* to support the ground troops after the droid parts were found, they might have gotten there not long before the Falcon even took off. So there could definitely be a big gap in their air superiority coverage, going off what's shown in the film.
This is precluding two possibilities: (1) that there was a permanent detachment of Star Destroyers at Tatooine, which I find unlikely given Obi Wan's decision to choose that as a hiding spot, or (2) that there are additional, unseen, Star Destroyers traveling with Vader during his chase with Leia, and that he left
three of them to merely pick up ground troops who'd been sent to secure the contents of any empty escape pod.