If I've got alcohol, how long can I survive without water?
Solution 1:
If you're dead-set on making due with this embark area, I would dig for the caverns. Pretty much just pick a point, and dig straight down. (If you grabbed the newest release, this has apparently been made easier by allowing designations that span z-levels.)
If you're just digging a small stairway, and not an elaborate 'grand central vein' as I usually do, it should be relatively fast to hit the caverns. I'd suggest having two dwarves dig out two side-by-side up/down stairs. This is more efficient than a single stair because they won't fight over who is digging where/when.
Once you hit the caverns, the first thing you see is almost always an underground lake. The second thing you almost always see is underground creatures. You may want to just grab a few buckets of water quickly, then floor up your stairs to keep them from surfacing, at least until you have a militia.
Once you have a fertile farmland, you never need to water it again, and can have infinite booze. You will, however, need water for tending wounded, so it might be worth building a well near the underground cavern. The bucket can drop down from the cavern ceiling, protecting you from all but flying creatures. Don't worry if the well is a hike - water is hopefully seldom used after farms are running.
Solution 2:
Without soil or water, your only recourse is to dig for the caverns. (Though if you really don't have soil, I wonder what those bushes you're harvesting are growing on).
It sounds like what might be happening is that you've harvested above ground plants, but since they haven't been consumed, you're not getting any seeds from them.
The simplest recourse in that case is to just brew some booze with the aboveground plants. Instant seeds. Do not cook them, as the seeds will get stuck in the biscuits, disappearing into the ether of dwarf beards and gullets.