Wormhole drive technology didn't exist when Destiny was launched
The Destiny was launched from Earth, some 50 million years ago.
Ancient wormhole drive technology was being developed on Atlantis, in their post-Earth civilization in the Pegasus Galaxy.
Gabriele writes: “3. Destiny is older than Atlantis. In “The Lost City” we come to know that Atlantis is about 30 million years old. The gate aboard Destiny is older than the ones in the Milky Way. In “Frozen” we come to know that the gates in the Mily Way are about 50 million years old. Is the Destiny about 60 million years old?”
Answer: Damn that’s old. If Destiny is older than the Milky Way gates then yes.
-Joseph Mallozi, Producer of Stargate Universe (and SGA & SG1), on his blog
So, we could be looking at a time difference between the technologies of 20-30 million years. As others have mentioned, the technology hadn't even been finished or used by the time the Ancients left Atlantis, but was finished by McKay for a relatively short hope from one galaxy to another. Keep in mind that Stargates could already be used to jump between galaxies with relative ease, using ZPMs, so it's a testament to the difficulty of the wormhole drive technology that it hadn't been used for in-galaxy or intergalactic jumps.
As to why they didn't later try to finish the technology anyway, one could argue it wasn't only because they achieved Ascension in the end, but prior to Ascension they were struggling with other issues, such as the war against the Wraith in the Pegasus galaxy.